Design of a Meta-Material with Targeted Nonlinear Deformation Response

130 Pages·2016·2.8 MB·English

Clemson University
TigerPrints
All Theses Theses
12-2015
Design of a Meta-Material with Targeted Nonlinear
Deformation Response
Zachary Satterfield
Clemson University, [email protected]
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Satterfield, Zachary, "Design of a Meta-Material with Targeted Nonlinear Deformation Response" (2015).All Theses.Paper 2245.
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DESIGN OF A META-MATERIAL WITH TARGETED
NONLINEAR DEFORMATION RESPONSE

A Thesis
Presented to
the Graduate School of
Clemson University

In Partial Fulfillment
of the Requirements for the Degree
Master of Science
Mechanical Engineering

by
Zachary Tyler Satterfield
December 2015

Accepted by:
Dr. Georges Fadel, Committee Chair
Dr. Nicole Coutris, Committee Member
Dr. Gang Li, Committee Member
ABSTRACT
The M1 Abrams tank contains track pads consist of a high density rubber. This
rubber fails prematurely due to heat buildup caused by the hysteretic nature of elastomers.
It is therefore desired to replace this elastomer by a meta-material that has equivalent
nonlinear deformation characteristics without this primary failure mode. A meta-material
is an artificial material in the form of a periodic structure that exhibits behavior that differs
from its constitutive material. After a thorough literature review, topology optimization
was found as the only method used to design meta-materials. Further investigation
determined topology optimization as an infeasible method to design meta-materials with
the targeted nonlinear deformation characteristics. Therefore, a method was developed in
this thesis to logically and systematically design meta-material unit cells using engineering
principles to achieve the desired nonlinear response. This method, called the Unit Cell
Synthesis Method, requires the designer to have a fundamental understanding of the
geometric nonlinearity of an elemental geometry. One or more of these elemental
geometries are then systematically combined into a unit cell. A size optimization is
performed on promising unit cell concepts to tune the geometry and converge its response
towards that of the target. Application of this method was successful in generating a meta-
material to meet the response of the rubber pad. The method represented in this thesis is
meant to serve as a framework for future designers to develop meta-materials for nonlinear
targeted responses.
ii
DEDICATION
To my family and friends.
iii
ACKNOWLEDGEMENTS
This research would not have been possible without the support and collaboration
from many individuals. I would like to thank my parents, Nathaniel and June, for their
unwavering support. I would not have made it this far without them. Thanks to my sister,
Heather, for her unrelenting competition and love that has motivated my success. Thanks
to Kara, who has unconditionally supported me throughout my research and the writing of
this thesis.
I would like to thank all of my committee members for contributing their
knowledge and support throughout this research project. I would like to thank Dr. Fadel
for providing me with this research opportunity and guiding me through the many stages
of the research process. Thanks to Dr. Li for his expertise in finite elements and the
enthusiasm he brought to this research. Thanks to Dr. Coutris for her expertise in elasticity
and attention to detail throughout this research.
I would like to thank Matthew Castanier, Bill Bradford, and the folks at US Army
TARDEC for their financial support of this research. I would also like to thank Christopher
Cardine of General Dynamics and Joshua Goossens of Tenneco for their collaboration and
providing an industrial perspective.
I would like to thank my lab-mates in EIB 136 and friends who have contributed to
this research. Thanks to Rahul Renu, Vijay Sarthy, and Anthony Garland for their
insightful discussions. Thanks to Neehar Kulkarni for his close collaboration and
discussion with this research.

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TABLE OF CONTENTS
Abstract ..................................................................................................................... ii
Dedication .................................................................................................................... iii
Acknowledgements ............................................................................................................ iv
Table of Tables ................................................................................................................ viii
Table of Figures ................................................................................................................. ix
Chapter 1. Introduction ..................................................................................................1
1.1. Overview of Abrams Military Track Pad System.................................................1
1.2. Motivation for Replacing Elastomer Track Pad ...................................................3
1.3. Motivation for Designing a Meta-Material ...........................................................6
1.4. Research Questions ...............................................................................................8
1.5. Thesis Outline .......................................................................................................9
Chapter 2. Literature Review.......................................................................................10
2.1. Methods to Design and Optimize Meta-Materials ..............................................10
2.2. Applications in Designing Meta- Materials ........................................................22
2.3. Conclusions .........................................................................................................26
Chapter 3. Designing via Topology Optimization.......................................................28
3.1. Objective .............................................................................................................28
3.2. TO in Optistruct ..................................................................................................28
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TABLE OF CONTENTS (CONTINUED)
3.3. Discussion ...........................................................................................................33
3.4. Conclusions .........................................................................................................40
Chapter 4. Designing via Engineering Principles ........................................................41
4.1. Objective .............................................................................................................41
4.2. Method of Evaluation .........................................................................................41
4.3. Design of the Brick Unit Cell .............................................................................46
4.4. Design of the BrickOval Unit Cell......................................................................52
4.5. Design Considerations ........................................................................................62
4.6. Conclusions .........................................................................................................70
Chapter 5. A Unit Cell Synthesis Method for Meta-Material Design .........................73
5.1. Method Introduction ...........................................................................................73
5.2. Method Description ............................................................................................75
5.3. Discussion ...........................................................................................................83
5.4. Conclusion ..........................................................................................................85
Chapter 6. Conclusions and Future Work ...................................................................87
6.1. Conclusions .........................................................................................................87
6.2. Broader Impact....................................................................................................88
6.3. Future Work ........................................................................................................89
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TABLE OF CONTENTS (CONTINUED)
Chapter 7. References ..................................................................................................91
Appendices ....................................................................................................................96
Appendix A. Python Script for Brick Design ..................................................................97
Appendix B. Python Script for BrickOval Design ........................................................106
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TABLE OF TABLES
Table 4.1 Target % Vertical Deformation Values .................................................45
Table 4.2 Full Factorial Parameters and Values ....................................................51
Table 4.3 Dimensions of Optimized UC................................................................61
Table 4.4 % Difference in Bulk Deformation Comparison Across Load Cases ...64
Table 4.5 Comparison of Bulk Deformation between Scaled Unit Cells ..............66
Table 5.1 Possible Connection Configurations ......................................................76

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TABLE OF FIGURES
Figure 1.1. Components of the T186LL Track Link [2] ..........................................1
Figure 1.2. 2D Representation of a Road Wheel and Track Link [3] ......................2
Figure 1.3. Track Backer Pad Failures Due to Chunking [2] ..................................3
Figure 1.4. Decaying of Elastomer Properties w.r.t. Cycling Stress [6] ..................4
Figure 1.5. Thermal Map of M1 Abrams Track Pad and Road Wheel [2] ..............5
Figure 1.6. Loading and Unloading Stress-Strain Curves for (Left) Elastomer, and
(Right) Linear Elastic Material [8] .............................................................6
Figure 1.7. Methodology to Optimize Meta-Material to Achieve target Properties
[10] ...............................................................................................................7
Figure 1.8. Ashby Chart Comparing Materials According to Loss Coefficient and
Young's Modulus [3,9] ................................................................................8
Figure 2.1. Microscopic Unit Cell Variables in Square Void [19] ........................11
Figure 2.2. Example (left) Boundary Conditions and (right) Solution using the HM
[22] .............................................................................................................13
Figure 2.3. Example Solutions of SIMP Method with (left) p=1.5 and (right) p=3
[22] .............................................................................................................14
Figure 2.4. The Effect of Varying “p” in the SIMP Method [23] ..........................15
Figure 2.5. Example of (left) a Polyhex Prototile and (right) a Parallelogram
Fundamental Domain of this Pattern [26] ..................................................18
Figure 2.6. Fundamental Domains for an L-Shaped Prototile [27] .......................18

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