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Thermal and deformation analysis of multiphase sulfur concrete extrusion for planetary construction

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Thermal and deformation analysis of multiphase sulfur concrete extrusion for planetary construction

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Content THERMAL AND DEFORMATION ANALYSIS OF MULTIPHASE SULFUR
CONCRETE EXTRUSION FOR PLANETARY CONSTRUCTION

By
Behnam Zahiri

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Astronautical Engineering)

May 2019

1

III
Abstract
Autonomous robotic construction using in-situ materials is an economically
viable and reliable option for extraterrestrial infrastructure buildup. Feasibility of such
approach has been successfully demonstrated in the case of ground-based prototypes
using Contour Crafting (CC), which is large-scale Additive Manufacturing technology.
Sulfur concrete, a waterless concrete that has numerous terrestrial applications and a
potentially ideal choice for planetary construction was chosen as the construction
material in the process. Sulfur is present in abundance on the surface of Mars and so
sulfur concrete can be prepared after processing in-situ regolith. Robotic construction
methods such as Contour Crafting can then utilize this sulfur concrete to deposit layers of
the concrete on top of each other to make structures, similar idea behind Additive
Manufacturing (AM) process. Our trials with sulfur-based concrete show strong promise.
The behavior of sulfur concrete during curing process is not known and yet it
directly impacts the quality of the structures made with this material. Only a few attempts
have been made in the literature to identify the mechanical properties of sulfur concrete
and still the deformation study of sulfur concrete which occurs before curing and under
thermal cooling is lacking in the literature. Hence, deformation of sulfur concrete during
curing process when it is transitioning from molten state to solid state due to thermal
cooling is studied. This research proposes a methodology to characterize deformation
behavior of sulfur concrete under thermal cooling during extrusion process in Contour
Crafting. This research includes numerical simulations and deformation analysis using
computational fluid dynamics (CFD) methods. In preliminary research the state transition

IV
of sulfur concrete from molten state to solid state under cooling with natural convection
is carried out using CFD models. Level set method was used to track the free surface of
material and to define material properties during this transition. The results of the
characterization have been used to optimize the profile shape of the outer nozzle to
enhance the shape of extrusion. Moreover, the results of this characterization have been
employed to predict the deformation and thermal cooling process of sulfur concrete
deposition layers under radiation cooling present in vacuum conditions for planetary
applications.

V
Table of Contents
Abstract .............................................................................................................................. III
List of Figures .................................................................................................................... VII
List of Tables ....................................................................................................................... X
1 INTRODUCTION ........................................................................................................... 1
1.1 Introduction to Additive Manufacturing (AM) and Contour Crafting ............................ 1
1.2 Sulfur concrete ................................................................................................................ 3
1.3 Statement of The Problem .............................................................................................. 4
1.4 Research Outline ............................................................................................................. 5
1.5 Research Contributions ................................................................................................... 6
1.6 Organization of the Dissertation ..................................................................................... 6
2 Background of The Study ............................................................................................ 8
2.1 Brief history of space exploration ................................................................................... 8
2.2 Introduction to Sulfur Concrete Contour Crafting .......................................................... 8
2.3 Sulfur Concrete.............................................................................................................. 10
2.3.1 Aggregates ............................................................................................................................. 11
2.3.2 Properties of sulfur concrete ................................................................................................. 12
2.3.3 Effect of Vacuum.................................................................................................................... 16
2.3.4 Effect of Freeze and Thaw ..................................................................................................... 17
2.4 Contour Crafting Extruder Development ...................................................................... 18
2.4.1 Auger-based Extrusion System .............................................................................................. 19
2.4.2 The latest developments in Contour Crafting extrusion systems ......................................... 23
2.4.3 6-DOF KUKA Robot ................................................................................................................ 26
2.4.4 Sulfur Concrete Deformation Test Bed Design ...................................................................... 28
2.5 CRITIQUE OF PAST APPROACHES ................................................................................. 30
3 Chapter Three: Modeling Approach ........................................................................ 32
Introduction ................................................................................................................................ 32
3.1 Governing Equations ..................................................................................................... 32
3.1.1 Fluid Flow ............................................................................................................................... 32
3.1.2 Level Set Method ................................................................................................................... 33
3.1.3 Non-Newtonian fluids ............................................................................................................ 35
3.1.4 Solidification Model ............................................................................................................... 37
3.2 Modeling the natural convection: ................................................................................. 39
3.2.1 Boussinesq Approximation: ................................................................................................... 39
3.3 Modeling Phase Change ................................................................................................ 40
3.4 CFD Simulation: ............................................................................................................. 41
3.4.1 Geometry of the Model ........................................................................................................ 42

VI
3.4.2 Boundary and Loading Conditions ........................................................................................ 43
3.4.3 Material ................................................................................................................................. 44
4 Chapter Four: Results ................................................................................................ 45
4.1 Analysis of Stage One results - Phase change and thermal cooling.............................. 45
4.2 Analysis of Stage Two results – Prediction of deformation in vacuum ........................ 51
4.2.1 Analysis of deformation for planetary habitat construction ................................................. 52
4.2.2 Analysis of nozzle geometry reconstruction on extrudate deformation .............................. 63
4.3 Analysis of Stage Three, experimental results .............................................................. 66
4.3.1 Materials for the extrusion .................................................................................................... 67
4.3.2 Linear printing process .......................................................................................................... 67
5 Chapter Five: Concluding Remarks .......................................................................... 70
5.1 Conclusion ..................................................................................................................... 70
6 REFERENCES .............................................................................................................. 73

VII
List of Figures
Figure 1.1. Contour Crafting assembly and fabricating process
Figure 1.2. Gantry robot structure for Contour Crafting
Figure 1.3. Contour Crafting space application
Figure 1.4. Sulfur concrete mobile production unit
Figure 2.1. Sulfur concrete contour crafting robot
Figure 2.2. Three layers extrusion sample made at Contour Crafting Cab
Figure 2.3. Comparison of composition of conventional concrete versus sulfur concrete
Figure 2.4. Sulfur concrete production process
Figure 2.5. Physical properties of aggregates and their quantitative analysis
Figure 2.6. Different compositions for sulfur concrete
Figure 2.7. Stress development of sulfur concrete vs conventional concrete
Figure 2.8. Stress-strain relationship for sulfur concrete vs conventional Portland concrete
Figure 2.9. Photographs of sulfur concrete samples for macro analysis: (a) before acid
resistance testing; (b) after 180 days in acid solution
Figure 2.10. Photographs of Portland cement concrete samples for macro analysis: (a)
before acid resistance testing; (b) after 60 days in acid solution
Figure 2.11. Sulfur concrete production process
Figure 2.12. Photograph of the vacuum chamber used for the sublimation experiments
Figure 2.13. (a–c) Microstructure of the 45 𝑤𝑡 % sulfur–silica binder and 55 𝑤𝑡 % JSC-1
(JSC-1 is a lunar regolith simulant made at Johnson Space Center) concrete samples. (a)
As-cast, (b) after 8 days in vacuum, (c) after 58 days in vacuum. Pressure level in the

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vacuum chamber was on the order of 5 × 10
−6
𝑡𝑜𝑟𝑟 (7 × 10
−4
). Spherical particles are
the silica grains
Figure 2.14. Extrusion Mechanisms
Figure 2.15. Auger-based extrusion system
Figure 2.16. Auger-based extrusion system with piezo vibrators
Figure 2.17. Sample made with Martian regolith simulant using auger-based extrusion
system
Figure 2.18. Auger worn out in the extrusion system after 50 hours of operation
Figure 2.19. The final extrusion system developed for SCCC
Figure 2.20. The development version of the final extrusion system for SCCC and the
samples made with this system
Figure 2.21. Contour Crafting for space application
Figure 2.22. Tool path of straight wall & half dome performed by KUKA robot
Figure 2.23. CAD file and the actual system for linear test bed designed for experiments
Figure 3.1. Variations of shear stress to shear rate dependency in different fluids
Figure 3.2. Shear stress and shear rate relation in a Bingham plastic
Figure 3.3. Phase transition function
Figure 3.4. 2-D cross section of the extrusion
Figure 3.5. Boundary and loading conditions
Figure 4.1. VOF model and the deformed state of sulfur concrete
Figure 4.2. Temperature distribution in the air
Figure 4.3. Velocity magnitude field through the air due to buoyancy and temperature
gradient

IX
Figure 4.4. Velocity vector field through the air due to buoyancy and temperature
gradient
Figure 4.5. Comparison between the deformed state obtained from numerical analysis
and experiment
Figure 4.6. Bilinear transition function approximation
Figure 4.7. Lunar base made with 3d printing
Figure 4.8. View factor between to elements of the surface 1 and surface 2
Figure 4.9. Final deformation of extruded material with radiation cooling
Figure 4.10. Final deformation of extruded material with radiation cooling and gravity of
the surface of the Moon
Figure 4.11. Composition of Atmosphere on Mars
Figure 4.12. Martian habitat
Figure 4.13. Sulfur concentration in the upper few decimeters of the Martian surface, as
mapped by the Mars Odyssey Gamma Ray Spectrometer
Figure 4.14. Final deformation of extruded material with radiation cooling and gravity of
the surface of the Mars
Figure 4.15. Different trapezoid shapes for nozzle profile
Figure 4.16. CFD model setup based on the optimal trapezoid for nozzle profile
Figure 4.17. Final VOF of deformation the optimal trapezoid for nozzle profile
Figure 4.18. The test bed used for experiments
Figure 4.19. Original (above) and trapezoidal nozzles
Figure 4.20. Experimental sample made with reconstructed nozzle profile

X
List of Tables
Table 2.1. KR150L KUKA robot parameters
Table 3.1. Material properties used for CFD analysis
Table 4.1. Modal proportions of Lunar minerals and glasses [82]
Table 4.2. Average abundance of elements in Lunar soil [82]
Table 4.3. Estimated Lunar Surface Temperatures [83]
Table 4.4. Lunar dust composition
Table 4.5. Materials and their percentage for preparation of sulfur concrete

1
1 INTRODUCTION
1.1 Introduction to Additive Manufacturing (AM) and Contour Crafting
Additive manufacturing (AM) is a manufacturing process in which 3D objects are
made by adding layer-upon-layer of material, the same process used in 3D printers. The
material used for making the object can be plastic, metal, concrete etc.
AM technologies normally require a 3D modeling software by which a CAD
model of the object is created and transferred to the printer machine.

(a) Assembly with top and side trowels (b) Ceramic printing by Contour Crafting
Figure 1.1. Contour Crafting assembly and fabricating process

Over the past three decades, additive manufacturing (AM), also widely known as
3D printing, has impacted traditional manufacturing industry for its specific capability in
rapid prototyping, fabrication of complex geometries, creation of multi-material
composites and product customization. Contour Crafting is an extrusion based additive
manufacturing process which can quickly build structures such as houses out of Portland
concrete (Figure 1.2,1.3) [18]. By depositing wet concrete through the nozzle outlet and
against side shaping trowel, Contour Crafting can create a smooth surface finish over the
accumulated successive thick layers [19]– [23].

2

Figure 1.2. Gantry robot structure for
Contour Crafting
Figure 1.3. Contour Crafting space
application

In the Mars and Lunar colonization missions planned by NASA, Contour Crafting
is considered to be the promising construction candidate for planetary construction,
especially in automatically building radiation shielding and shade walls, protective
hangars for equipment and shelter for astronauts [18], [24]– [26]. Taking advantage of
the sulfur material that naturally exists on the Martian and Lunar surfaces, Sulfur
Concrete Contour Crafting (SCCC) is regarded as an in-situ resource utilization (ISRU)
technology [27]– [31]. It should be noted that the gantry structure is less attractive for
planetary construction because of the large size of the gantry which makes fitting it in
cargo compartment of launch vehicle problematic and has implementation problems due
to the requirement of autonomous assembly of the gantry upon deployment. Accordingly,
a mobile robotic system such as the one shown in Figure 1.3 is proposed which will be: a)
more compact when its elements are retracted hence making it more suitable for
launching, b) is possible to deploy much easier after being landed, and c) is able to build
structures with practically unlimited size [28].

3
1.2 Sulfur concrete
Conventional concrete is comprised of sand, coarser aggregate, and a binder agent
based on calcium silicate. Addition of water to this mixture triggers a chemical reaction
which causes the binding to happen, after which the mixture is hardened into what is
known as concrete. Sulfur concrete, on the other hand, consists only of aggregates and
sulfur, a thermoplastic material, and does not rely on a chemical reaction to form. Sulfur
acts as a binding agent in sulfur concrete and basically after being heated melts and binds
aggregates and after cooling down hardens into sulfur concrete in a reversible process.
Sulfur concrete is widely used in industry specially for construction and has high viability
for applications in environments subjected to salt and acid [1-17]. It shows great
compressive strength (higher than conventional concrete), low water permeability and
fast curing time.

Figure 1.4. Sulfur concrete mobile production unit [1]

Sulfur concrete meets NASA’s ISRU (In-Situ Resource Utilization) requirements
for some Lunar and most Martian structure construction by means of Contour Crafting
(CC). The performance of sulfur concrete is sensitive to its ingredients and to the
variables in the thermal process used for applying the material. The sulfur concrete

4
extrusion process is implemented on a mini-scale auger extruder and a novel full-scale
extruder.

1.3 Statement of The Problem
Achieving structures with better qualities and precision in Contour Crafting with
sulfur concrete requires characterization of sulfur concrete and study of its curing process
during thermal cooling of sulfur concrete. The curing process for sulfur concrete is a
thermal process which involves phase change and is totally different from the curing
process of regular concrete. Molten sulfur concrete cures as it undergoes a transition from
molten state to solid state due to thermal cooling through natural convection.
During this solidification process, sulfur concrete undergoes deformation. The
faster the cooling process after the extrusion, the less deformation is observed in the
extruded sulfur concrete. Study of this deformation under thermal cooling is essential in
achieving structure with better quality and more precision. Additionally, based on our
experiments some parameters of the extrusion system can also impact the accuracy of
extruded layers.
Some of the parameters of the extrusion system are the reservoir and nozzle
temperature, the shape of the nozzle, the extrusion speed and back pressure. Back
pressure is the amount of pressure the cross-section of the fluid is experiencing at the
very end of the passage. An experiment is designed to quantitatively study the
deformation of the sulfur concrete extrusion under thermal gradient. Additionally, a
theoretical model is developed for the transition of the molten sulfur concrete into the
solid state and is verified using finite element analysis and computational fluid dynamics.

5
The results of the theoretical model and CFD model are used to predict the deformation
of the extruded under different thermal conditions. The results of the characterization
have been used to optimize the profile shape of the nozzle to enhance the shape of
extrusion. Moreover, the results of this characterization have been employed to predict
the deformation and thermal cooling process of sulfur concrete deposition layers under
radiation cooling present in vacuum conditions for planetary applications. The results are
essential for planetary construction using in-situ materials.

1.4 Research Outline
This study Following are the objectives of this proposal:
1. The proposed research utilizes available tools and techniques to characterize
sulfur concrete composite and its post-extrusion behavior during its curing via
thermal cooling process. The first research objective is to develop a methodology
to investigate the governing equations behind thermal cooling through natural
convection and phase change of sulfur concrete to model the deformation of the
extruded materials in the Contour Crafting process, SCCC.
2. The second objective is to use the characterization model to chance the profile of
the outer nozzle to counteract the deformation and enhance the topology of the
extrusion.
3. One of the potential applications of sulfur concrete-based Contour Crafting,
SCCC, besides terrestrial construction, is the autonomous planetary constructions
specifically on the Moon and Mars which their regolith is naturally resourceful in
sulfur. The third objective of the study is to create a model that can be used to

6
predict the behavior of extrusion, specifically thermal cooling through radiation in
planetary applications.

1.5 Research Contributions
Based on the review of the available literature, this research provides a novel
approach to study sulfur concrete through characterization of its thermal cooling process
and phase change. This work offers a methodology for investigating the deformation of
sulfur concrete extrusion which is also useful in quality control of Sulfur Concrete based
Contour Crafting, SCCC. Characterization of sulfur concrete is essential specifically for
space construction and for studying its behavior in different environment such as
different atmospheric pressures and temperatures. Studying the effects of nozzle profile
geometry on the final shape of the extrusion is also novel and the experiments show the
accuracy of the characterization.
The simulation and characterization of sulfur concrete has been utilized to both
predict the behavior (setting geometry) of this material in vacuum condition and also in
enhancing the geometry of the extrudate by changing the profile of the extrusion nozzle.
It is demonstrated that by changing the geometry of the extrusion nozzle from a
rectangular profile to a trapezoidal profile, the deformation can be reduced to achieve a
rectangular final geometry for the cured extruded part.
1.6 Organization of the Dissertation
Chapter 1: This chapter includes an introduction to sulfur concrete, its application in
Contour Crafting and its properties and curing process.

7
Chapter 2: This chapter reviews all fundamentals associated with sulfur concrete. The
critiques of the past approaches and the research gap are covered in this chapter.
Chapter 3: This chapter presents the methodology utilized for carrying out research in
studying the deformation and thermal cooling of sulfur concrete extrusions made by
Contour Crafting during sulfur concrete curing process. The methodology is categorized
into three stages. In Stage One, the preliminary simulation model for studying the phase
change and thermal cooling of sulfur concrete under natural convection is developed. In
Stage Two, the results of the characterization of Stage One is utilized to predict the
deformation and thermal changes of sulfur concrete in vacuum conditions and on the
surface of the Moon and Mars. In Stage Three, the characterization results of Stage One
are utilized to reconstruct the geometry of the extrusion profile to counteract the
deformation and enhance the geometry of the final extrusion.
Chapter 4: The analysis of the results of all aforementioned three stages are presented in
this chapter. For Stage One, the preliminary results are gathered, and characterization was
achieved. For Stage Two, prediction of deformation is made using the characterization
model of Stage One. And for Stage Three, experimental results are presented based on a
new and reconstructed geometry for the nozzle profile.
Chapter 5: This chapter discusses the accomplished results and the area of contribution
as well as the suggestions for future research direction.

8
2 Background of The Study
2.1 Brief history of space exploration
The first know idea to reach the outer space was proposed by the Soviet scientist
Konstantin Tsjolkoysky in the article “The Exploration of Cosmic Space by Means of
Reaction Devices,” published in 1903 [32,33]. The first rocket to reach the space was the
V-2 rocket, launched by the Germans during the World War II [34]. Yuri Gagarin was
the first cosmonaut to reach the upper space in 1961. Neil Armstrong was the first man,
who has landed on the Moon surface along with Buzz Aldrin in 1969.
Mankind has always had the dream to conquer and colonize the space, and the Moon
because of its vicinity to earth was often considered as the first potential destination. The
Moon has plenty of valuable natural resources [35] and it could be a great base for future
launch vehicles that are going to explore deeper into space [36]. Among the very specific
conditions Lunar gravity is almost one sixth of the Earth gravity and lunar days are about
twenty-nine Earth days. Lunar atmosphere provides almost no protection against
radiation [37]. Mars on the other hand also has lower gravity compared to earth and
vacuum condition is also present on Mars.
2.2 Introduction to Sulfur Concrete Contour Crafting
The Sulfur Concrete Contour Crafting (SCCC) is a construction scale 3D printing
technology which uses sulfur concrete. Sulfur concrete has the advantage of not needing
water to create and having acceptable strength specially for Lunar and Martian
construction, high acid/salt resistance and long durability [38]. The experimental SCCC
machine designed and developed by B. Khoshnevis and X. Yuan [29-30] is equipped
with a 6-axis robot and a novel sulfur concrete extruder and has the capability to build on

9
complex terrain. This technology has the potential to construct in outer spaces and in
environments such as Mars or Moon, since both are abundant in sulfur which has been
proven after the discovery of mineral troilite (FeS) on the Moon [39-41]. Processing
troilite to elemental sulfur and viability of using sulfur concrete on the Moon has been
previously studied [42-48]. It was reported that it takes approximately 6 years for a 1cm
layer of sulfur concrete to sublimate in vacuum conditions present on the Moon and Mars
[40].
In the SCCC process the sulfur concrete composite materials (elemental sulfur,
sulfur modifier, coarse aggregate and fine aggregate) are pre-melted and mixed at 150℃,
and are kept in the reservoir for one hour until the elemental sulfur reaches its desirable
state [38]. Then the well-prepared sulfur concrete is delivered to and deposited by a
special mixer/extruder fixed on a 6-axis robot. Sulfur concrete is deposited on the
calculated path and cures in less than 10 minutes. After 24 hours, the construction made
by sulfur concrete reaches its highest strength [48].

Figure 2.1. Sulfur concrete contour crafting
robot [29-30]
Figure 2.2. Three layers extrusion
sample made at Contour Crafting Cab
[29-30]

10
2.3 Sulfur Concrete
Sulfur has been used for quite a long time primarily as a bonding agent and its use
has been reported in the literature of ancient Egypt, Greece, China and India [49-52].
Sulfur concrete is referred to as a mixture of sulfur (as the binder) and a variety of
aggregates. Use of sulfur concrete in construction has been reported since 1920s [53].
Naturally occurring heavy aggregates such as sand, gravel, stone chips or ballast can be
used in making sulfur concrete as well as naturally occurring or synthetic light
aggregates.
After heating up the mixture of aggregate and sulfur the mixture is cooled down
whereupon the mixture solidifies and gains hardness comparable to hydraulic concrete.
Some of the unique properties of sulfur concrete include rapid strength development,
high ultimate strength, low permeability, and superior resistance to strong acids and
saline solutions.
However, the main shortcoming of this sulfur concrete (in which the used sulfur
was in its elemental form without any modifications) is a high shrinkage volume that
occurs when the formed article cools to ambient temperature.
Such high shrinkage frequently results in distortion as well as inaccurate final
dimensions, which is unacceptable in blocks used in a mortarless building system that
must be producible with accurate predetermined dimensions.
Fig 4.3 compares the composition of the Portland cement concrete and sulfur concrete.
Sulfur concrete typically has 12 − 22 wt. % sulfur and the rest are aggregates of
different size. Additives of different kinds, usually plasticizers, can also be added, up to
5%, in order to enhance the properties of sulfur concrete such as bending strength. Sulfur

11
melts at 115℃ and the process of making sulfur concrete typically happens at 135℃ to
155℃.

Figure 2.3. Comparison of composition of conventional concrete versus sulfur concrete
[38]

Figure 2.4. Sulfur concrete production process [38]

2.3.1 Aggregates
Aggregates used in making sulfur concrete can be of different types including
different grain size sand, gravel, ash etc. Sulfur concrete has been used for many years in
the construction of acid conduits because of their superior acid resistance. Typical
compressive strength of 33 − 47MPa was achieved in 6-12 hours after solidification
when the lime stone aggregate was used in the production of sulfur concrete [54-57].

12

Figure 2.5. Physical properties of aggregates and their quantitative analysis [38]

Figure 2.6. Different compositions for sulfur concrete [38]

2.3.2 Properties of sulfur concrete
2.3.2.1 Sulfur Concrete Compressive Strength
Sulfur concrete has superior properties compared to hydraulic concrete that
advantageous for specific applications. Maximum strength for Portland cement concrete

13
is achieved only after several weeks, approximately 28 days to achieve 90% of final
strength, whereas sulfur concrete achieves its final strength only after a few hours, and
moisture and temperature do not influence the development of strength [38], Figure 2.7.
The compressive strength of sulfur concrete ranges between 40 − 50 MPa.

Figure 2.7. Stress development of sulfur concrete vs conventional concrete [38]
2.3.2.2 Strength Development for Elemental Sulfur Concrete
Figure 2.8 shows the comparison between the stress strain curve of Portland
cement versus sulfur concrete. [58,59]. The compressive strength of Portland cement
concrete increases as strain increases, to approximately 0.017 and reaches a maximum
value of 20 𝑀𝑃𝑎 . Then, it decreases.
However, for elemental sulfur concrete, the compressive strength continues to
increase with the strain in excess of 0.025 reaching a value of approximately 40 𝑀𝑃𝑎 .

14

Figure 2.8. Stress-strain relationship for sulfur concrete vs conventional Portland
concrete [38]

2.3.2.3 Corrosion Resistance
Sulfur concrete has high corrosion resistance properties and is widely used in civil
constructions where conventional concrete fails to perform [60-62]. If sulfur concrete is
specifically made for applications where corrosion resistance is a requirement then the
selection of aggregates used in its composition during its production should be made
according to a specific standard. In acidic environments, aggregates of sulfur concrete
should not exhibit any signs of pores, and so the aggregates for sulfur concrete
production should be selected such that when tested for 24 hours in an acidic
environment of expected concentration, they exhibit less than two percent weight
reduction. Similar standard is applied to selection of aggregates for applications in saline
environment which in which aggregates should not show any reaction or deterioration
after testing for 24 hours in saline environment of expected concentration.

15
4.
Figure 2.9. Photographs of sulfur concrete samples for macro analysis: (a) before acid
resistance testing; (b) after 180 days in acid solution [63]

Figure 2.10. Photographs of Portland cement concrete samples for macro analysis: (a)
before acid resistance testing; (b) after 60 days in acid solution [63]

Additionally, properties of sulfur concrete, specifically its corrosion resistance,
are enhanced by using fillers and different additives such as fly ash and fiberglass in its
composition [64-69]

Figure 2.11. Sulfur concrete production process [38]

16
2.3.3 Effect of Vacuum
Behavior of sulfur concrete has been studied over the last years [70] and has been
an important subject from the construction perspective [71].
The Moon is surrounded by a vacuum environment; pressure on the Moon is about
10
−12
𝑇𝑜𝑟𝑟 (1.33 ∗ 10
−10
𝑃𝑎 ). This environment may affect the preparation of various
construction materials, which are chemically or molecularly unstable in such
environment [71].
As mentioned earlier, sulfur concrete is a viable construction material on the
Moon. Different experiments have been carried out with sulfur concrete samples in
vacuum conditions and some degradation was observed on the surface during the 58 days
period due to sublimation of sulfur. However, the rate of sublimation was observed to
decrease with time [72].

Figure 2.12. Photograph of the vacuum chamber used for the sublimation experiments
[70]

17

Figure 2.13. (a–c) Microstructure of the 45 𝑤𝑡 % sulfur –silica binder and 55 𝑤𝑡 %
JSC-1 (JSC-1 is a lunar regolith simulant made at Johnson Space Center) concrete
samples. (a) As-cast, (b) after 8 days in vacuum, (c) after 58 days in vacuum. Pressure
level in the vacuum chamber was on the order of 5 × 10
−6
𝑡𝑜𝑟𝑟 (7 × 10
−4
).
Spherical particles are the silica grains [38].

2.3.4 Effect of Freeze and Thaw
Sulfur concrete was proven to be reliable in environments with extremely low
temperatures. In a study, sulfur concrete samples were tested in an experiment under
constant freezing temperature of −27℃ and also under cyclic freeze-thaw conditions and
no significant reduction in strength was reported [73]. Moreover, sulfur limestone
aggregate concrete also shows sufficient resistance to damage by freeze-thaw cycles [73].

18
2.4 Contour Crafting Extruder Development
Over the past decade, different mechanisms have been considered, developed and
used as the extrusion system in Contour Crafting, primarily for extrusion of Portland
cement [78]. Development of a novel extrusion system specifically for sulfur concrete
which could provide the thermal requirements for the preparation of the mixture was
necessary. The system should also withstand environments such as the Moon and Mars
[79].

(a) Different extrusion systems
(b) Bridging effect
Figure 2.14. Extrusion Mechanisms [30]

Figure 2.14 shows different extrusion mechanisms that were developed for
Contour Crafting. All the developed extrusion systems work based on the principle which
is to first create a compression and back pressure and another mechanism to eliminate the
bridging effect when extruding the material through a heated profile to shape the
extrusion.
The bridging effect is referred to the interlocking of particles across the walls of
the conduit which carries the concrete. This bridging effect creates a barrier against the
flow of the material and is created at different levels along the conduit carrying the

19
material. Bridging effect makes it extremely hard and, in some cases, impossible for the
material to flow and as a result material blockage will occur. Bridging effect naturally
happens when a granular viscous material is flowing through a tubular passage. When
bridging effect is present the back pressure required to ensure material flow is extremely
high and, in most cases, ineffective.
The function of the compression mechanism is to feed the mixture to the
extrusion nozzle. As it is shown in Figure 2.14, these mechanisms can differ in the way
they provide these functions. Figure 2.14(a) show an auger-based extrusion mechanism,
followed by a double-roller mechanism (Figure 2.14(b)) followed by a reciprocal
(plunger) method showed in (c) and a propeller stirring method, shown in (d). Each
generation of these mechanisms have some merits over their predecessors and in some
cases minor drawbacks.
2.4.1 Auger-based Extrusion System
Auger-based extrusion system was one of the very first generation of the
extrusion systems that was developed by J. Zhang PhD for sulfur concrete Contour
Crafting (SCCC). In this mechanism, a rotating auger inside a barrel pushes the material
down by its rotation. The barrel is heated and kept at a certain temperature throughout the
process. This mechanism is shown on Figure 2.15.

20

(a) Auger-based extrusion developed for
SCCC
(b) Diagram of the auger-based
system
Figure 2.15. Auger-based extrusion system [30]

In this device a motor rotates the auger that pushes the dry mixture of regolith and
sulfur into the heated barrel and finally through the nozzle-head, which shapes the final
extrusion. In order to prevent the clogging, the auger has been also equipped with a
vibrator.
Another version of the same system was also developed by J. Zhang PhD with
piezo-vibrators that would induce vertical vibrations along the auger combined with a
second horizontal vibration exerted to the nozzle head (Figure 2.16). The combination of
these two vibrations would prevent the formation of bridging phenomenon and help with
the friction during extrusion process.

21

Figure 2.16. Auger-based extrusion system with piezo vibrators [30]

Some of the samples made with the developed auger-based extrusion mechanism
is also shown in Figure 2.17.

22

Figure 2.17. Sample made with Martian regolith simulant using auger-based
extrusion system [30]

One of the major drawbacks of using auger-based extrusion system is the
durability of the auger as the main moving part inside the system. The auger, being in
constant contact and high friction with the granular and hard mixture of sulfur and
Martian regolith had always went through high abrasion to the point that after only 50
hours of work most of the teeth of the auger would completely wear away. Figure 2.18
shows how the auger was worn out in one of these systems after only 50 hours of work

23

Figure 2.18. Auger worn out in the extrusion system after 50 hours of operation
[30]

2.4.2 The latest developments in Contour Crafting extrusion systems
The latest extrusion system developed by B. Khoshnevis for SCCC which has
also proven to be the most successful one so far is shown in Figure 2.19. The system
includes a reservoir and a mixing system. The reservoir ensures the mixtures of sulfur
concrete is always ready and the mixer ensures that the mixture is uniform and is ready
for extrusion. Thermal solution around the reservoir and throughout the extrusion nozzle
ensure a constant temperature for the mixture along the entire process. A DC motor with
the help of a gear box provides rotation to a shaft and a propeller which makes the
material flow to the extrusion nozzle where the extrudate is pushed through a rectangular
nozzle profile and ultimately exits the system and forms the extrudate.

24

Figure 2.19. The final extrusion system developed for SCCC [30]

The feasibility and reliability of the extrusion mechanism was first evaluated by
creating a simple version of the same extrusion system shown in Figure 2.20. A fuzzy
logic control system for the motor ensures constant rotation speed and steady material
extrusion. A three-layer sample made by X. Yuan PhD with this extrusion system is also
shown in Figure 2.20.

25

Figure 2.20. The development version of the final extrusion system for SCCC and
the samples made with this system [30]

This development version extrusion system was made as a linear extrusion system
only to proof concept reliability of the mechanism before the final extrusion system was
developed. After successful experiments with the linear test bench (Figure 2.20), the final
extrusion system (Figure 2.19) capable of printing curved samples was developed. The
entire extrusion system shown in Figure 2.19 was installed on the end-effector arm of a 6-
axis KUKA industrial robot. The system also includes a monitoring unit consisting of a
scanner and a camera. The camera primarily records the extrusion process and the
scanner dynamically scans the shape and quality of the extrudate sending feedback to the
controller unit of the motor and the robot.

26

2.4.3 6-DOF KUKA Robot
I order to build structures in full-scale a 6-axis KUKA industrial robot is used as
the moving arm for the extrusion system. The extrusion is system is mounted to the end-
effector of this robot. This robot consists of six rotational actuators which provide six
degrees of freedom. For future developments this robot can be mounted on top of a rover
to provide even more mobility and larger workspace.

(a) KR150 KUKA robot (b) CC robot on JPL rover
Figure 2.21. Contour Crafting for space application [30]

Figure 2.21 (a) shows the KUKA robot and Figure 2.21 (b) shows the Contour
Crafting robot mounted on top of the JPL rover. Some of the parameters and details of
the KR150L KUKA robot used in Contour Crafting is listed in table 2.1.

27

Table 2.1. KR150L KUKA robot parameters
Voltage 480V
Capacity 150KG
Repeatability ±0.12mm
Horizontal Reach 2410mm
Vertical Reach 2700mm
Axis Robot Motion Range Robot Motion Speed
1-Axis ±185° 110 °/s
2-Axis +93 to -40 110 °/s
3-Axis +155° - 119° 110 °/s
4-Axis ±350° 170 °/s
5-Axis ±125° 170 °/s
6-Axis ±350° 238 °/s

28

Figure 2.22. Tool path of straight wall & half dome performed by KUKA robot [30]

2.4.4 Sulfur Concrete Deformation Test Bed Design
In order to observer the deformation of the extrusion under different nozzle
profile and validate Stage Three of this research, a linear extrusion system was developed
by Xiao Yuan.
This test bed is comprised of a linear actuator that pushes the material through a
square conduit and then the material exits the nozzle. The extrusion square-shape tube
and the linear actuator, along with the thermal solutions around the tube and the nozzle

29
are all mounted on a linear rail that moves the nozzle on a linear path with a constant
speed.
The thermal solution is comprised of several flexible resistive heaters around the
tube and nozzle and are controlled by a PID temperature controller. The material is fed to
the tube and then is pushed down by the linear piston while the system is moved linearly
on the test bed by a steppers motor rotating at a constant speed. A camera positioned in
front of the extrusion nozzle captures the entire process and records the deformation of
the extruded material. Figure 2.23 shows the CAD file along with the actual test bed
system.

30

Figure 2.23. CAD file and the actual system for linear test bed designed for
experiments

Using this system, the effects of changing the nozzle geometry on the deformation
of the extrusion was studied and compared to the results of the CFD analysis.

2.5 CRITIQUE OF PAST APPROACHES
The previous research projects on sulfur concrete have been mainly focused on
the experimental aspects and viability of using sulfur concrete both for terrestrial and
planetary applications. Almost no research has been carried out to characterize sulfur
concrete. No previous research on sulfur concrete has focused on shape stability. No
previous research has investigated the analytical model of the curing process of sulfur
concrete which is the result of thermal cooling and phase change inside sulfur concrete.
No previous research on CC has focused on the effects of the geometry of the nozzle
profile on the geometry on the final extruded part. And no previous research has been

31
conducted to predict the deformation and behavior of sulfur concrete in extremely low
temperatures in particular similar to conditions found on the lunar surface for planetary
applications.

32
3 Chapter Three: Modeling Approach
Introduction
This chapter discusses the preliminary work done on numerical analysis and
modeling of sulfur concrete during phase change process through thermal cooling.

3.1 Governing Equations
3.1.1 Fluid Flow
Flow of molten sulfur concrete which results in the deformation of the extruded
section before it gets completely cured, can be modeled by the Navier-Stokes equations
for the incompressible flow, coupled with the continuity equation.
ρ
∂𝐮 ∂t
− ∇. μ(∇𝐮 + (∇𝐮 )
T
) + ρ(𝐮 . ∇)𝐮 + ∇p = F
Equation 3.1
∇. 𝐮 = 0 Equation 3.2
In Navier-Stokes equation, as described by Eq. (3.1), 𝐮 is the material’s velocity,
p is material’s pressure, ρ is material’s density, μ is dynamic viscosity and the term F
accounts for the external forces applied to the material including volumetric buoyancy
force and surface tension effects which are used to model the solidification of sulfur
concrete. Eq. (3.2) is the continuity equation. The Navier-Stokes equation represents the
conservation of momentum, whereas the continuity equation represents the conservation
of mass. As it will be described later, the interface between the extruded sulfur concrete
and the surrounding air, as well as the interface between the sulfur concrete and the

33
ground or layer beneath it, are modeled using Eulerian approach in a fixed grid.
Therefore, the positions of theses interfaces are not explicitly calculated and hence there
was no need for mesh generation at these interfaces.

3.1.2 Level Set Method
In order to track the free surface at the liquid-gas interface, Level Set method is
used in this research. This method has been described by Sussman et. al. [74,75] as
follows:
In the Level Set method, a scalar function ϕ is defined such that it has negative
values for liquid phase and has value of zero at the interface and positive values for gas
phase. This scalar function relates to the fluid flow by the following equation:
∂ϕ
∂t
+ 𝐮 . 𝛁 ϕ = 0
Equation 3.3
Properties of air and fluid phase can be described in terms of the level set function
as follows:
ρ = ρ
g
+ H(ϕ)(ρ
l
− ρ
g
) Equation 3.4
μ = μ
g
+ H(ϕ)(μ
l
− μ
g
) Equation 3.5
k = k
g
+ H(ϕ)(k
l
− k
g
) Equation 3.6
where H(ϕ) is a smooth heavy side function defined and is defined as:
H(ϕ) =
1 + tanh(−
ϕ
n
)
2

Equation 3.7

34
In Equation 3.7, H(ϕ) equals to 1 for the liquid phase (molten concrete) and
equals to 0 for the gaseous phase (ambient air) and its value smoothly changes at the
interface. Variable n is a hyper-parameter controlling the characteristics of the transition
zone.
In order to account for the surface tension, a source term was added as to the
Navier-Stokes equations acting only at the interface:
F
ST
= γκδ(ϕ)𝐧 Equation 3.8
where F
ST
is a vector field of the surface tension force, γ is the surface tension, κ is the
curvature of the interface surface, δ(ϕ) is the Dirac delta function and 𝐧 is the unit vector
normal to the surface of interface. By using a smooth Dirac delta function around the
width of the interface we can further simplify Equation 3.8 [75].
δ(ϕ) =
n
2
√π
e
−n
2
2
.ϕ
2

Equation 3.9
The normal vector and the curvature at the gas liquid interface can be calculated
in terms of the level set function as described by Equation 3.10 and 3.11 and will be used
to find the shape of the interface:
𝐧 =
𝛁 ϕ
|𝛁 ϕ|
Equation 3.10
κ = 𝛁 .
𝛁 ϕ
|𝛁 ϕ|

Equation 3.11

35
3.1.3 Non-Newtonian fluids
Sulfur concrete is a non-Newtonian fluid. In incompressible Newtonian fluids the
shear stress is proportional to the deformation rate as described by Newton’s law of
viscosity (Equation 3.12).
τ = μ(
∂𝑢 𝑗 ∂𝑥 𝑖 +
∂𝑢 𝑖 ∂𝑥 𝑗 )
Equation 3.12
In Equation 3.12, 𝝉 is the shear stress and 𝛍 is the viscosity. In Newtonian fluids,
viscosity, 𝛍 is invariant to the shear rate that the fluid is experiencing.
In non-Newtonian fluids, however, shear stress is not proportional to the shear rate and
viscosity is not a constant and changes as the fluid experiences different stresses. Based
on the behaviors that fluids exhibit in terms of their shear rate with respect to the shear
stress they experience, they are classified into different categories as shown in Figure 3.1.

Figure 3.1. Variations of shear stress to shear rate dependency in different fluids

Rheological properties of uncured sulfur concrete are very similar to that of
Bingham plastics, that is, uncured sulfur concrete does not show any shear rate in low

36
stresses but after a certain threshold of shear stress is surpassed the concrete slowly starts
to exhibit shear rate in its layers. This is a common characteristic of Bingham plastics in
which the shear stress and shear rate are related by the following equation:

τ = τ
0
+ μ𝛾 ̇ Equation 3.13

In Equation 3.13, 𝛕 𝟎 is the yield stress. Properties of Bingham plastic for different
regimes of shear rates is shown in Figure 3.2.

Figure 3.2. Shear stress and shear rate relation in a Bingham plastic

Bingham plastic model is used in this research to model the rheologic properties
of sulfur concrete which is inherently related to its viscosity. The effects of temperature
on sulfur concrete’s viscosity is modeled by considering a temperature-dependent
multiplier 𝐻 (𝑇 ) for viscosity, as described by the following equation:
μ = μ
0
𝐻 (𝑇 ) Equation 3.14
In this equation, 𝐻 (𝑇 ) determines the temperature dependency of viscosity. The function
𝐻 (𝑇 ) was defined as:

37
𝐻 (𝑇 ) = exp (𝛼 (
1
𝑇 − 𝑇 0
−
1
𝑇 𝛼 − 𝑇 0
)) Equation 3.15
𝛼 =
𝐸 𝑅 Equation 3.16
In Equation 3.15, 𝑇 0
is the temperature shift and was chosen to be zero, and 𝑇 𝛼 is the
reference temperature and 𝛼 is defined in Equation 3.16 and is the ratio of activation
energy, 𝐸 , to thermodynamic constant, 𝑅 .

3.1.4 Solidification Model
In order to model the solidification process, the Voller and Prakash [76] model is
used in this research but instead of writing the heat equation in terms of enthalpy, the heat
equation is written in terms of temperature:
ρ. c
p
∂T
∂t
+ ∇. (−k∇T + ρ. c
p
T𝐮 ) = 0
Equation 3.17
Equation 3.17 is valid for all three phases, solid, liquid and gas. The change in
properties of each phase is captured by Equations 3.4 to 3.6.
The solid fraction function, F
s
, is defined as a function of temperature such that it has a
value of zero for all temperatures below the solidus temperature and equals to 1 for
temperatures above the liquidus temperature and has a value between 0 and 1 for all
temperatures in the transition zone. F
s
is defined as follows:
F
s
(T) = {
0
(T
m
+ ε − T)/2ε
1

T ≥ (T
m
+ ε)
(T
m
− ε) ≤ T < (T
m
+ ε)
T < (T
m
− ε)

Equation 3.18

38
In this equation 2ε = T
Liquidus
− T
Solidus
and T
m
=
T
Liquidus
+T
Solidus
2
is the average
temperature.
The solidification model assumes the fluid flow in the transition range is similar
to the flow in a porous media. The porosity function is defined in terms of temperature
as:
λ = 1 − F
s
(T) Equation 3.19
For all temperatures such that T > T
Liquidus
= T
m
+ ε we have λ = 1 and for all
temperatures T < T
solidus
= T
m
− ε we have λ = 0.
A solidification term in terms of the porosity is then added to the Navier-Stokes
equation as follows:
𝐅 s
= −A𝐮 Equation 3.20
Where:
A =
C(1 − λ)
2
(λ
3
+ q)
Equation 3.21
In Equation 3.21, C and q are hyper-parameters. For temperature above the liquidus
temperature, 𝜆 = 1 and 𝐴 = 0, and no modification is made to the Navier-Stokes
equations and the flow corresponds to the flow of a fully fluid phase. However, when the
temperature is below the solidus, 𝜆 = 0 and A takes a very high value (𝐴 = 𝐶 /𝑞 ),
dominating the transient, diffusive and convective terms of Equation 3.1, forcing the
velocity to be zero. For all the temperatures in between, 𝜆 is between 0 and 1, and the
Navier-Stokes equations are corresponding to the flow in a porous medium.

39
3.2 Modeling the natural convection:
In order to account for the heat transfer between molten sulfur concrete and
surrounding air and the resulting cooling effect that happens based on that, equations of
natural convection have been added to the model. For this purpose, instead of solving the
full compressible formulation of the Navier-Stokes equations, which can be
computationally expensive, an approximation of the non-isothermal flow for natural
convection as defined by Boussinesq approximation has been considered.
3.2.1 Boussinesq Approximation:
The Navier-Stokes equations for a compressible fluid is defined as:
ρ

(
∂𝐮 ∂t
+ 𝐮 . ∇𝐮 ) = −∇p + ∇. (μ(∇𝐮 + (∇𝐮 )
T
)) −
2
3
μ(∇. 𝐮 )𝐈 + ρ𝐠 Equation 3.22
In this equation, 𝐮 is the fluid velocity, p is the fluid pressure, ρ is the fluid density, μ is
the fluid dynamic viscosity, 𝐈 is the identity matrix, and 𝐠 is the acceleration due to
gravity [77].
The Navier-Stokes equations are solved together with the continuity equation:
1
ρ
Dρ
Dt
+ ∇. 𝐮 = 0 Equation 3.23
In Boussinesq approximation, density variation is only considered for the
buoyancy term, ρ𝐠 and neglected for all other terms. The Boussinesq approximation
results in:
ρ
0
(
∂𝐮 ∂t
+ 𝐮 . ∇𝐮 ) = −∇p + ∇. (μ(∇𝐮 + (∇𝐮 )
T
)) −
2
3
μ(∇. 𝐮 )𝐈 + ρ𝐠 Equation 3.24

40
Where a constant density, ρ
0
, is used in the body force term corresponding to the
buoyancy force, to replace the temperature and pressure-dependent density ρ.
Another effect of using Boussinesq approximation is that in continuity
equation,
1
ρ
Dρ
Dt
+ ∇. 𝐮 = 0, since the magnitude of
1
ρ
Dρ
Dt
would be small with respect to the
velocity gradients, ∇. 𝐮 , the continuity equation can be reduced to that of an
incompressible form ∇. 𝐮 = 0. This also simplifies the Navier-Stokes equations since the
term −
2
3
μ(∇. 𝐮 )𝐈 in Navier-Stokes equations would be zero and also since the
viscosity, μ, is generally assumed to be constant, the diffusion term, ∇. (μ(∇𝐮 +
(∇𝐮 )
T
)), can thus be written as μ∇
2
𝐮 and the Navier-Stokes equation becomes [77]:
ρ
0
(
∂𝐮 ∂t
+ 𝐮 . ∇𝐮 ) = −∇p + μ∇
2
𝐮 + ρ𝐠 Equation 3.25
The buoyancy term 𝐮 can be written as (ρ
0
+ ∆ρ)𝐠 , where ∆ρ = ρ −
ρ
0
represents the density variation with respect to the reference density ρ
0
. Hence:
ρ
0
(
∂𝐮 ∂t
+ 𝐮 . ∇𝐮 ) = −∇p + μ∇
2
𝐮 + (ρ
0
+ ∆ρ)𝐠 Equation 3.26
Also, we the buoyancy term ∆ρ𝐠 = (ρ − ρ
0
)𝐠 , can be written as (ρ − ρ
0
)𝐠 =
−ρ
𝟎 β(T − T
0
)𝐠 , where β is the coefficient of thermal expansion. For ideal gases, β =
1/T
0
and so −ρ
0
β(T − T
0
)𝐠 = −ρ
0
(T − T
0
)/T
0
𝐠 .
ρ
0
(
∂𝐮 ∂t
+ 𝐮 . ∇𝐮 ) = −∇p + μ∇
2
𝐮 + ρ
0
𝐠 − ρ
0
(T − T
0
)/T
0
𝐠 Equation 3.27
3.3 Modeling Phase Change

41
In order to model the phase change within sulfur concrete, a phase transition
function has been defined which governs the change in material properties as the sulfur
concrete cools down from molten phase to the solid state, Figure 3.3. The rate of this
transition in material properties is one of the hyper-parameters of the analysis that will be
verified by experiments.

Figure 3.3. Phase transition function [77]

3.4 CFD Simulation:
In order to model the Computational Fluid Dynamics in ANSYS, four models are
required: Incompressible Navier-Stokes, convection diffusion, convection conduction and
general PDE weak form for phase model. The variables of the Navier-Stokes model are
u , v and p. The variable of the convection diffusion model is ϕ. The variable of the
convection conduction model is T and the variable of the phase model is λ.

42
3.4.1 Geometry of the Model
In order to carry out the numerical analysis, a two-dimensional rectangular cross
section of the extrusion was considered as the model. The boundary conditions were
selected as follows: the lower surface of the extrusion has a frictional contact with the
surface beneath it, corresponding to the ground surface. This face of the cross section was
also considered to have a constant temperature due to contact with the ground, and the
temperature was considered to be equal to the ambient room temperature, 23℃.
Three remaining faces of the cross section were chosen to be free surfaces, and
the thermal boundary conditions for these faces are driven by the interaction with the
surrounding ambient air. The initial temperature of ambient air was chosen to be the
room temperature, 23℃.

Figure 3.4. 2-D cross section of the extrusion

43
3.4.2 Boundary and Loading Conditions
The lower face of the extrusion is in contact with the ground or the layer beneath,
hence the boundary condition for this face was chosen as a fixed displacement. The
temperature of this face was also chosen to be constant and equal to room temperature,
23℃. The boundary conditions for the three faces of the section exposed to ambient air
were chosen as one of free surfaces and their initial temperature was equal to the
temperature of extrusion right after coming out of nozzle, 145℃. The heat is dissipated
from the extrudate to ambient air through theses faces. The flow of heat flux within air is
occurred through natural convection governed by the Navier-Stokes equations and
buoyancy forces. The only force acting within the extruded section is the force exerted by
gravity.

Figure 3.5. Boundary and loading conditions

44

3.4.3 Material
The material properties for different phases used in the CFD numerical analysis is
summarized in table 3.1.

Table 3.1. Material properties used for CFD analysis
Phase
Property air liquid solid
𝜌 (
𝑘𝑔
𝑚 3
)
1.3 2382
𝜇 (𝑃𝑎 . 𝑠 ) 4.79 ∗ 10
−5
1.15 ∗ 10
−3
--
𝛾 (
𝑁 𝑚 ) 0.793 ∗ 10
−4
--
𝑘 (
𝑊 𝑚 ℃
) 0.024 104
𝑇 𝑚 (℃) -- 660
𝜀 (℃) -- 5
L(
J
Kg
) -- 3.97 ∗ 10
5

𝐶 𝑝 (
𝐽 𝐾𝑔 . 𝐾 ) 1005 1090

45
4 Chapter Four: Results
This section presents the results of the three stages described in previous chapters.

4.1 Analysis of Stage One results - Phase change and thermal cooling
A two-dimensional cross section of extruded sulfur concrete going through
natural convection cooling and phase change was simulated. The final deformed state and
shape of the extrusion was obtained as depicted in Figure 4.1. Figure 4.1 shows the VOF
(volume of fluid) for the air (gaseous phase) versus sulfur concrete (liquid phase) and is
color coded based on the discretization of the extreme phases where the value 0 belongs
to the air phase and value of 1 belongs to sulfur concrete. Moreover, the intermediate
phase, the interface between air and sulfur concrete, is characterized by the gradient of
change of values in the discretization plane in VOF model and is colored in green.

Figure 4.1. VOF model and the deformed state of sulfur concrete

46

The results of Boussinesq approximation model is shown in Figure 4.2 where the
flow of air due to temperature gradient and the resulting buoyancy is shown. This figure
clearly shows the effect of natural convection cooling in setting the state of the extrusion.

47

Figure 4.2. Temperature distribution in the air

48
Figure 4.3 and Figure 4.4 respectively show the velocity magnitude field and
velocity vector field where the formation of vortices due to buoyancy difference resulting
from thermal gradient and natural convection throughout the air can be seen.

49

Figure 4.3. Velocity magnitude field through the air
due to buoyancy and temperature gradient

50

Figure 4.4. Velocity vector field through the air
due to buoyancy and temperature gradient

The comparison between the results of numerical model and experiment is shown
is Figure 4.5. It can be seen that the numerical model can predict the final deformed
shape obtained from experiment.

Figure 4.5. Comparison between the deformed state obtained from
numerical analysis and experiment

It also should be noted that the transition function used for the phase change has
been approximated by a bilinear function in the transition zone, Figure 4.6.

51

Figure 4.6. Bilinear transition function approximation

This transition function is the characterization of phase change for sulfur concrete
as it cools down which determines the final deformation and heat transfer throughout its
solidification process.

4.2 Analysis of Stage Two results – Prediction of deformation in vacuum
The transition function for the sulfur concrete has been established in the previous
section. This characterization will be used in Stage Two of the analysis to predict the
deformation of the extrusion in vacuum conditions as well as preforming prediction in
order to reconstruct the outer nozzle profile geometry in order to counteract the
deformation and enhance the extruded geometry after solidification.
The foundation for performing the prediction in vacuum condition is to simulate
the conditions in Lunar and Martian habitat construction, hence a brief introductory
section for the specific condition present on these planets are also provided.

52

4.2.1 Analysis of deformation for planetary habitat construction
The surfaces of the Moon and Mars are largely covered with loose,
unconsolidated rock material known as regolith. Smaller particles (sub-centimeter), also
known as soil or dust, can be problematic for both machines and humans. Lunar and
Martian dust has adversely affected rotating machinery and has the potential to interfere
with ECLSS hardware –clogging filters, interfering with pressure seals, etc.
The section below discusses the results of deformation under the Lunar and
Martian conditions and the specific environment that applies to each of them.

4.2.1.1 Lunar conditions
This section covers some of the environmental conditions specific to the Moon
related to this study. Different aspects of Lunar environment such as Lunar minerals,
regolith and temperature considerations is discussed in this chapter.

4.2.1.1.1 Lunar Minerals
Lunar environment has a variety of mineral compounds and glasses. Glasses are
solids that have similar compositions to minerals except that they lack internal atomic
structure. Lunar glasses have originated by two main processes, meteoroid impact and
volcanic eruptions. The rocks on the Moon have mineral compositions that is very similar
to the minerals Earth however they differ from Earth rocks with their complete lack of
water and common presence of metallic iron, 𝐹𝑒
0
. There are two major groups of
minerals on the Moon, silicate and oxide minerals. Silicate minerals, with their main
components silicon (Si) and oxygen (O), make up over 90%, by volume, of most lunar

53
rocks. Table 4.1 shows the average volume percentages of minerals in regolith collected
at the Apollo and Luna landing sites [82, 83]

Table 4.1. Modal proportions of Lunar minerals and glasses [82]
Mineral Type Modal Proportions
[𝑽𝒐𝒍 − %]
Plagioclase 12.9 − 69.1
Pyroxene 8.5 − 61.1
Olivine 0.2 − 17.5
Silica 0.0 − 1.7
Ilmenite 0.0 − 12.8
Mare Glass 0.9 − 17.2
Highland Glass 3.8 − 25.0

4.2.1.1.2 Lunar Regolith
Most of our information about the Lunar environment is coming from the Lunar
regolith. Lunar regolith is originated from two different processes: from the continuous
impact of meteoroids on the lunar surface and the steady bombardment of the lunar
surface by plasma particles coming from the Sun.
Studies on returned samples have shown that the majority of the lunar regolith
consists of particles less than 1 cm in size. Lunar regolith is a somewhat cohesive, dark
grey to light grey, very-fine-grained and loose material. The mean grain size of analyzed
Lunar regolith ranges from about 40𝜇𝑚 to about 80𝜇𝑚 and averages at 60𝜇𝑚 . Oxygen

54
is the most abundant element in lunar surface materials. Table 4.2 presents the elements
in their order of abundance, both in [atom-%] and [weight-%]. [83]

Table 4.2. Average abundance of elements in Lunar soil [82]
Element Average abundance
[𝒂𝒕𝒐𝒎 − %]
Average abundance
[𝒎𝒂𝒔𝒔 − %]
Sites
O 60% 45% Maria / Highlands
Si 16.6% 21% Maria / Highlands
Al 10% 13% Highlands
5% 5% Maria
Ca 5% 10% Highlands
4.5% 8% Maria
Mg 5% 5.5% Maria / Highlands
Fe 2.5% 6% Highlands
6% 15% Maria
Ti < 1% < 1% Maria / Highlands
Na < 1% < 1% Maria / Highlands

4.2.1.1.3 Lunar Surface Temperature
In general, the lunar surface temperature increases by about 280 K from just
before lunar dawn to lunar noon. The temperature at lunar noon varies throughout the
year because of varying distance from the Sun. There is a large difference in mean
temperature, i.e. the temperature averaged over a complete day-night cycle, just below
the lunar surface. Estimated average surface temperatures and temperature extremes for

55
different areas of the Moon were made by the Lunar Colony Study Group and are
presented in Table 4.3 [83].

Table 4.3. Estimated Lunar Surface Temperatures [83]
Shadowed
Polar
Craters
Other
Polar
Areas
Front
Equatorial
Back
Equatorial
Limb
Equatorial
Typical
Mid-Latitudes
Average
Temperature
40 𝐾 220 𝐾 254 𝐾 256 𝐾 255 𝐾 220 𝐾 − 255𝐾
Monthly Range
None 10 𝐾 140 𝐾 140 𝐾 140 𝐾 110 𝐾

Figure 4.7. Lunar base made with 3d printing [87]

In order to predict the deformation of material in applications for Lunar
constructions, conditions specific to the Moon is considered. Average grain size of
analyzed lunar soils is between 60 and 80μm with 20% less than 20μm (by comparison a
grain of fine beach sand is 90μm). Lunar dust has very low electrical conductivity and is

56
prone to building up electrostatic charge, with subsequent electrostatic deposition. Lunar
dust is hard, abrasive and easily embedded in loose-weave fabrics. Lunar dust
composition is shown in Table 4.4:
Table 4.4. Lunar dust composition
𝑆𝑖 𝑂 2
50%
𝐴𝑙
2
𝑂 3
15%
𝐶𝑎𝑂 10%
𝑀𝑔𝑂 10%
𝑇𝑖𝑂 2
5%
𝐹𝑒 (+𝑁𝑎 , 𝐾 , 𝐶𝑟 , 𝑍𝑟 ) 5 − 15%

Lack of atmosphere and partial gravity of about 1/6 g, are the two distinctive
characteristics of the Lunar environment from heat transfer standpoint. Lack of
atmosphere on the Moon leaves radiation and conduction through the lower layers as the
only modes of heat transfer between the extruded material and the environment.
The average temperature on the Moon varies between 110℃ during the day to
about −183℃ during the night. The dark sky above Lunar surface at night acts as a
perfect black body for any object radiating heat.
Radiation heat transfer between two surfaces is governed by the following
equation
𝐸 = 𝜀𝜎 𝑇 4

57
Where 𝐸 is the total rate of energy emitted via radiation per unit surface area, 𝜀 is
the surface emissivity, 𝜎 is the Stefan–Boltzmann constant and 𝑇 is the temperature of
the surface. This equation can be generalized to the case where there is radiation heat
transfer between multiple surfaces in space each with a different orientation and each pair
having a specific view angle. This general equation in the case of two surfaces in space
and simplified as a black body has the following form:
𝑄 ̇ 1→2
= 𝐴 1
𝐸 𝑏 1
𝐹 1→2
− 𝐴 2
𝐸 𝑏 2
𝐹 2→1

Where 𝑄 ̇ 1→2
is the rate of heat transfer from the first surface to the second
surface, 𝐸 𝑏 is the energy flux per unit surface area and can be obtained using Equation
4.1 as
𝑃 𝐴 for the two surfaces respectively, and 𝐹 1→2
is the view factor from the first
surface to the second surface.

Figure 4.8. View factor between to elements of the surface 1 and surface 2

View factor 𝐹 1→2
can be defined by taking surface elements from the two
surfaces, as shown in Figure 4.8, and can be defined by the following equation.

58
𝐹 1→2
=
𝑐𝑜𝑠 𝜃 1
𝑐𝑜𝑠 𝜃 2
𝜋 𝑠 2
𝑑 𝐴 2

Where 𝐹 1→2
is the view factor of two differential areas of areas 𝑑 𝐴 1
and 𝑑 𝐴 2
at a
distance 𝑠 , and 𝜃 1
and 𝜃 2
are the angle between the surface normals and the line
connecting the two elements on the surfaces. The total view factor between the two
surfaces can be derived as:

𝐹 1→2
=
1
𝐴 1
∫

𝐴 1
∫
cos𝜃 1
cos𝜃 2
𝜋 𝑠 2
𝑑 𝐴 2
𝑑 𝐴 1

𝐴 2

Using these equations, the total outward radiation heat flux transferring through
the free surface of the extruded sulfur concrete can be estimated as:
𝑄 ̇ = (𝐴 11
+ 𝐴 12
+ 𝐴 13
)𝜀𝜎 𝑇 4

Where 𝐴 11
, 𝐴 12
and 𝐴 13
are the three free surfaces of extruded sulfur concrete
exposed to the sky. The results of the CFD analysis for radiation cooling of sulfur
concrete under the vacuum conditions on the Moon is shown in Figure 4.9. For the sake
of comparing the final deformation of the extrusion with the case of natural convection
cooling, Figure 4.9 does not consider the difference in gravity on the surface of the
Moon.

59

Figure 4.9. Final deformation of extruded material with radiation cooling

The gravity on the surface of the moon however is about 1/6
th
of the gravity on
Earth and as a result this lower gravity directly impacts the final deformation of extruded
material. The CFD results of radiation cooling on the surface of the Moon and
considering the gravity of 1.62
𝑚 𝑠 2
on the surface of the Moon is presented in Figure 4.10.

Figure 4.10. Final deformation of extruded material with radiation cooling and
gravity of the surface of the Moon

60

Comparing the CFD results for the final deformation of extruded material, curing
under convection cooling with the case where the material is in vacuum and cures under
radiation cooling considering reduced gravity and under the gravity of Earth reveals an
interesting fact, that although the rate of heat transfer in vacuum with radiation cooling is
less than that of convection cooling which will result in more deformation of extruded
material before fully curing, the reduced gravity present on the surface of the Moon will
be the dominant factor in producing an overall reduced deformation before the material
fully cures and cools down.

4.2.1.2 Martian environment
Mars has an atmosphere that is mostly comprised of carbon dioxide. 𝐶 𝑂 2

accounts for 95.9% of the entire Martian atmospheric constituents, Figure 4.11. The
atmospheric pressure on the Martian surface averages 600 pascals [81]. Given the
presence of a low-pressure atmosphere and nearly twice the gravity of the Moon, Mars
dust contamination control should be easier with regards to the machinery and ECLSS.

61

Figure 4.11. Composition of Atmosphere on Mars [81]

The sulfur cycle is arguably the most important geochemical cycle on
Mars. The presence of sulfur-rich compositions on Mars is suggested by meteorite data,
in-situ bulk chemical and mineralogical analyses, remote sensing data from dust and
surfaces, and geochemical models [84].

Figure 4.12. Martian habitat [88]

X-ray fluorescence analyses from the Viking missions, almost forty years ago,
revealed that Mars has S- and Cl-rich surface regolith [83]. The red color of the soils

62
suggested that 𝑆 6+
likely predominates and that the S is hosted in sulfates. Subsequent
landed missions confirmed high S contents using APXS instruments: either an alpha-
proton X-ray spectrometer (Pathfinder mission) or an alpha-particle X-ray spectrometer
(Mars Exploration Rover, MER, mission) [84].
𝑆 𝑂 3
accounts for 6.8 𝑤𝑡 % (2.7 𝑤𝑡 % S) of Martian regolith which is higher than
the average S content of the top few tens of centimeters of the global Martian surface
(𝑆 𝑂 3
= 4.4 𝑤𝑡 %), mapped using the Gamma Ray Spectrometer (GRS) on the 2001
Mars Odyssey spacecraft, Figure 4.13. Overall, available data and findings are consistent
with the suggestion that S has been extensively transported and deposited across the
Martian surface [85].

Figure 4.13. Sulfur concentration in the upper few decimeters of the Martian surface,
as mapped by the Mars Odyssey Gamma Ray Spectrometer [84, 85]

Since Mars's atmosphere is about a hundred times thinner than the Earth's, it
doesn’t have the comparable capacity to retain heat energy. On average, the temperature
on Mars is about −80 ℉ (−60 ℃). In winter, near the poles temperatures can get down

63
to −195 ℉ (−125 ℃). During summer, temperature can get as high as 70 ℉ (20 ℃)
near the equator, and as low as −100 ℉ (−73 ℃). NASA's Mars Curiosity rover
measured air temperatures as high as 43 ℉ (6 ℃) in the afternoon, with temperatures
above freezing for a significant number of days.
The results of deformation under the Martian conditions are presented in Figure
4.14. As evident from the final deformation in Figure 4.14, partial gravity is still the
dominant factor on causing the final deformation, in other words, although the thin
atmosphere of Mars does not provide much capacity for heat dissipation from the
extruded material which should result in more deformation, the partial gravity helps
making the final deformation less than terrestrial conditions.

Figure 4.14. Final deformation of extruded material with radiation cooling and
gravity of the surface of the Mars

4.2.2 Analysis of nozzle geometry reconstruction on extrudate deformation
In previous sections deformation of extruded material, which is a results of
molten material flow before it completely solidifies, was encountered. In this section we

64
investigate the effects of nozzle profile on deformation. In order to counteract this
phenomenon and achieve better final geometries that are closer to a rectangular shape.
The geometry of the nozzle profile is changed from the default rectangular shape and
using the characterization model achieved in Stage One analysis we attempt to
reconstruct the geometry to counteract the extrusion deformation and have minimal
deformation at the end of the solidification process.
In order to achieve the optimal geometry for the nozzle profile, the transition
function in Stage One was employed within the CFD analysis and different classes of
trapezoid geometries were considered for the nozzle profile. Results of final deformations
for each profile were obtained based on the CFD analysis. The edges of the deformed
geometries were compared with a perfect undeformed profile and the profile geometry
with the least deformation was selected as the optimal profile.
The experimental validation for the deformation, carried out in Stage Three, was
based on this nozzle profile and the deformation of the final cured extrusion was
compared with the results of the CFD analysis for verification. In order to set up the
analysis of deformation for different nozzle profile different classes of the trapezoid
geometries as shown on Figure 4.15 were considered.

65
Figure 4.15. Different trapezoid shapes for nozzle profile

Comparing the results of CFD for all different geometries within the design space
shows that the optimal deformation happens for the trapezoid profile for which the upper
edge is 5𝑚𝑚 longer than the lower edge. The results of the CFD analysis for this profile
is shown in Figure 4.16, 4.17.

Figure 4.16. CFD model setup based on the optimal trapezoid for nozzle profile

66

Figure 4.17. Final VOF of deformation the optimal trapezoid for nozzle profile

4.3 Analysis of Stage Three, experimental results
This section presents the results of the nozzle profile reconstruction which have been
validated by conducting experiments using the physical test bed system shown in Figure
4.18. This test bed has been developed by X. Yuan. The results of the experiments have
been compared with the results of the CFD analysis.

Figure 4.18. The test bed used for experiments

67
4.3.1 Materials for the extrusion
The material constituents and their proportion for the preparation of sulfur
concrete is provided in Table 4.5.

Table 4.5. Materials and their percentage for preparation of sulfur concrete
Material Percentage
Pure elemental sulfur %35
Sand 500𝜇𝑚 %52.5
Ash %12.5

The sulfur concrete used in the experiments were based on %35 weight content of
sulfur and %65 weight content of aggregates. The aggregates used are a combination of
sand and ash. The particles in sand were measured to be no more than 500𝜇𝑚 in size
using a mesh to filter the particles. Ash was also used as one of the ingredients for the
aggregates. The amount of ash content used accounted for %12.5 of the weight of the
mixture. Ash gives the mixture a paste-like texture and makes the extrusion process more
robust by absorbing the excess liquid sulfur. Ash ingredient is primarily composed of
gypsum (𝐶𝑎𝑆 𝑂 4
. 2𝐻 2
𝑂 ).

4.3.2 Linear printing process
The printing process starts by preheating the aggregates up to a temperature of
160℃ and then mixing them with sulfur. After preliminary mixing, the mixture was kept
in furnace at a constant temperature of 145℃ for about 75 minutes. After this step the

68
mixture became ready for extrusion and was fed to the linear extruder. During the
printing process the linear piston actuator pushes down the mixture while a stepper motor
moves the nozzle at a constant speed along the extrusion path.
As mentioned in Chapter 3, the nozzle profile was also changed from a rectangular shape
to a trapezoid profile, as shown in Figure 4.19. A sample from the experiments with
reshaped nozzle profile is shown in Figure 4.20.

Figure 4.19. Original (above) and trapezoidal nozzles

Figure 4.20. Experimental sample made with reconstructed nozzle profile

Figure 4.20 shows the sample made with the reconstructed nozzle. As it is evident
from the cross section of the samples, the final set shape is very close to a rectangular

69
shape which validates the characterization model derived from the first stage of this
study. It has to be also mentioned that the geometric tolerances associated with sulfur
concrete in general, are extremely hard to control and are usually in the range of ±1𝑚𝑚
and the experimental results were achieved by the predictions of the characterization
model for a single nozzle shape that minimizes the deviation of samples from a
rectangular section.

70
5 Chapter Five: Concluding Remarks
5.1 Conclusion
The purpose of this research is to characterize the properties of sulfur concrete
during its curing process which involves phase change process as a result of thermal
cooling. The major objectives of this work were:
• To come up with an appropriate model that takes the solidification process
thermal effects into consideration
• To establish methodology that characterizes the behavior of sulfur concrete during
phase change
• To study the behavior of sulfur concrete in planetary applications
• To study the effects of geometry of the extrusion nozzle on the final deformation
of sulfur concrete
• To create a guideline for future users of Contour Crafting with sulfur concrete.
This study was conducted in three stages that are mutually connected. The results of
stage one was used as the basis for the analyses conducted in stage two and stage three.
The summary of each stage of the study is listed below:
• Stage One: This stage led the effort to achieve a characterization model for sulfur
concrete that lays the foundation for the following stages of this study. The
underpinning equations for this characterizations model are the Navier-Stokes
equations coupled with heat transfer equations and conservation of mass. By
factoring in a phase transition function to account for the change in the material
properties of sulfur concrete during thermal cooling as well as utilizing level set
method to track the free surface of the extrusion, the deformation model was

71
completed. The hyper-parameters of the model as well as the transition function
were set through an iterative process by comparing the analytical model and the
experimental results.
• Stage Two: Stage Two is a predictive approach that uses the characterization
model achieved in Stage One to find the deformation of extrusion under different
conditions. Specifically aimed at planetary applications of Contour Crafting for
construction of Lunar and Martian habitat, this stage tries to predict the
deformation of sulfur concrete on Lunar surface where there is lack of atmosphere
and on Martian surface where carbon dioxide is the dominant constituent of
atmosphere.
• Stage Three: This stage aimed to study the effects of extrusion nozzle geometry
on the final deformation of the extruded material after the solidification process.
In particular in this chapter the geometry of the nozzle was modified in order to
counteract the flow of the extrusion and the resulting deformation. To use the
characterization model to counteract the deformation before solidification original
rectangular nozzle profiles were changed and different trapezoidal geometries
were considered and fine-tuned to get the minimum final deformation after
solidification.
5.2 Future Work
The following suggestions are made for the direction of future works in this field:
• Sulfur concrete exhibits minute extents of shrinkage during its thermal cooling
and solidification process. The results of the CFD analysis can be enhanced by
factoring in shrinkage as well.

72
• With full characterized model of sulfur concrete, as proposed by this study, the
extrusion nozzle can be designed in such a way that it can automatically monitor
the extruded free surface and to reactively adapt itself, based on the methodology
put forward in Stage Three, to counteract the deformation and minimize the final
deformation.
• Future experiments can be carried out by following the exact constituents of
Lunar and Martian regolith in terms of particle size and chemical compositions.
• Future experiments can be carried out in vacuum environment to compare with
the CFD results.
• Effects of partial gravity on the machinery used in Contour Crafting should be
studied. This may involve various consideration:
o The hazardous effects of the fine regolith which move even more freely
under partial gravity and don’t settle, combined with their electrostatic
effect, on the moving parts of Contour Crafting System
o The effects of partial gravity on the back pressure and the flow of material
inside the nozzle

73
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Abstract (if available)

Abstract Autonomous robotic construction using in-situ materials is an economically viable and reliable option for extraterrestrial infrastructure buildup. Feasibility of such approach has been successfully demonstrated in the case of ground-based prototypes using Contour Crafting (CC), which is large-scale Additive Manufacturing technology. Sulfur concrete, a waterless concrete that has numerous terrestrial applications and a potentially ideal choice for planetary construction was chosen as the construction material in the process. Sulfur is present in abundance on the surface of Mars and so sulfur concrete can be prepared after processing in-situ regolith. Robotic construction methods such as Contour Crafting can then utilize this sulfur concrete to deposit layers of the concrete on top of each other to make structures, similar idea behind Additive Manufacturing (AM) process. Our trials with sulfur-based concrete show strong promise. ❧ The behavior of sulfur concrete during curing process is not known and yet it directly impacts the quality of the structures made with this material. Only a few attempts have been made in the literature to identify the mechanical properties of sulfur concrete and still the deformation study of sulfur concrete which occurs before curing and under thermal cooling is lacking in the literature. Hence, deformation of sulfur concrete during curing process when it is transitioning from molten state to solid state due to thermal cooling is studied. This research proposes a methodology to characterize deformation behavior of sulfur concrete under thermal cooling during extrusion process in Contour Crafting. This research includes numerical simulations and deformation analysis using computational fluid dynamics (CFD) methods. In preliminary research the state transition of sulfur concrete from molten state to solid state under cooling with natural convection is carried out using CFD models. Level set method was used to track the free surface of material and to define material properties during this transition. The results of the characterization have been used to optimize the profile shape of the outer nozzle to enhance the shape of extrusion. Moreover, the results of this characterization have been employed to predict the deformation and thermal cooling process of sulfur concrete deposition layers under radiation cooling present in vacuum conditions for planetary applications.

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Creator Zahiri, Behnam (author)

Core Title Thermal and deformation analysis of multiphase sulfur concrete extrusion for planetary construction

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Astronautical Engineering

Publication Date 04/24/2021

Defense Date 03/08/2019

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag 3D printing,contour crafting,deformation analysis,habitat,Lunar,Mars,Martian,Moon,multiphase,OAI-PMH Harvest,planetary construction,regolith,robotics,sulfur concrete,thermal

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Khoshnevis, Behrokh (committee chair), Erwin, Dan (committee member), Kunc, Joseph (committee member)

Creator Email be.zahiri@gmail.com,bzahiri@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-145401

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Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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