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Research Papers: Design Automation

Unit Cell Synthesis for Design of Materials With Targeted Nonlinear Deformation Response

[+] Author and Article Information
Zachary Satterfield

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: zsatter@g.clemson.edu

Neehar Kulkarni

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: neehark@g.clemson.edu

Georges Fadel

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: fgeorge@clemson.edu

Gang Li

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: gli@clemson.edu

Nicole Coutris

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: coutris@clemson.edu

Matthew P. Castanier

Analytics-Computational Methods & System
Behavior (CMSB) Team,
U.S. Army Tank Automotive Research,
Development, and Engineering Center (TARDEC),
Warren, MI 48397
e-mail: matthew.p.castanier.civ@mail.mil

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 15, 2016; final manuscript received August 29, 2017; published online October 3, 2017. Assoc. Editor: Nam H. Kim.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Mech. Des 139(12), 121401 (Oct 03, 2017) (11 pages) Paper No: MD-16-1764; doi: 10.1115/1.4037894 History: Received November 15, 2016; Revised August 29, 2017

A systematic unit cell synthesis approach is presented for designing metamaterials from a unit cell level, which are made out of linearly elastic constitutive materials to achieve tunable nonlinear deformation characteristics. This method is expected to serve as an alternative to classical Topology Optimization methods (solid isotropic material with penalization or homogenization) in specific cases by carrying out unit cell synthesis and subsequent size optimization (SO). The unit cells are developed by synthesizing elemental components with simple geometries that display geometric nonlinearity under deformation. The idea is to replace the physical nonlinear behavior of the target material by adding geometric nonlinearities associated with the deforming entities and thus, achieve large overall deformations with small linear strains in each deformed entity. A case study is presented, which uses the proposed method to design a metamaterial that mimics the nonlinear deformation behavior of a military tank track rubber pad under compression. Two unit cell concepts that successfully match the nonlinear target rubber compression curve are evaluated. Conclusions and scope for future work to develop the method are discussed.

Copyright © 2017 by ASME
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References

Walser, R. M. , 2001, “ Electromagnetic Metamaterials,” Proc. SPIE, 4467, pp. 1–15.
Larsen, U. D. , Sigmund, O. , and Bouwstra, S. , 1997, “ Design and Fabrication of Compliant Micromechanisms and Structures With Negative Poisson's Ratio,” J. Microelectromech. Syst., 6(2), pp. 99–106. [CrossRef]
Galgalikar, R. , 2012, “ Design Automation and Optimization of Honeycomb Structures for Maximum Sound Transmission Loss,” Master's thesis, Clemson University, Clemson, SC.
Guest, J. K. , and Prévost, J. H. , 2007, “ Design of Maximum Permeability Material Structures,” Comput. Methods Appl. Mech. Eng., 196(4–6), pp. 1006–1017. [CrossRef]
Sigmund, O. , and Torquato, S. , 1997, “ Design of Materials With Extreme Thermal Expansion Using a Three-Phase Topology Optimization Method,” J. Mech. Phys. Solids, 45(6), pp. 1037–1067. [CrossRef]
Sigmund, O. , Torquato, S. , and Aksay, I. A. , 1998, “ On the Design of 1-3 Piezocomposites Using Topology Optimization,” J. Mater. Res., 13(4), pp. 1038–1048. [CrossRef]
Bendsøe, M. P. , and Kikuchi, N. , 1988, “ Generating Optimal Topologies in Structural Design Using a Homogenization Method,” Comput. Methods Appl. Mech. Eng., 71(2), pp. 197–224. [CrossRef]
Bendsøe, M. P. , and Sigmund, O. , 2004, Topology Optimization: Theory, Methods, and Applications, Springer, Berlin.
Gibiansky, L. V. , and Sigmund, O. , 2000, “ Multiphase Composites With Extremal Bulk Modulus,” J. Mech. Phys. Solids, 48(3), pp. 461–498. [CrossRef]
Czech, C. , Guarneri, P. , and Fadel, G. , 2012, “ Meta-Material Design of the Shear Layer of a Non-Pneumatic Wheel Using Topology Optimization,” ASME Paper No. DETC2012-71340.
Berglind, L. A. , and Summers, J. D. , 2014, “ Direct Displacement Synthesis Method for Shape Morphing Skins Using Compliant Mechanisms,” ASME Paper No. DETC2010-28546.
Fazelpour, M. , and Summers, J. D. , 2013, “ A Comparison of Design Approaches to Meso-Structure Development,” ASME Paper No. DETC2013-12295.
Yoder, M. , Satterfield, Z. , Fazelpour, M. , Summers, J. D. , and Fadel, G. , 2015, “ Numerical Methods for the Design of Meso-Structures: A Comparative Review,” ASME Paper No. DETC2015-46289.
Wang, F. , Sigmund, O. , and Jensen, J. S. , 2014, “ Design of Materials With Prescribed Nonlinear Properties,” J. Mech. Phys. Solids, 69(1), pp. 156–174. [CrossRef]
Sigmund, O. , 1994, “ Materials With Prescribed Constitutive Parameters: An Inverse Homogenization Problem,” Int. J. Solids Struct., 31(17), pp. 2313–2329. [CrossRef]
Sigmund, O. , 1995, “ Tailoring Materials With Prescribed Elastic Properties,” Mech. Mater., 20(4), pp. 351–368. [CrossRef]
Cheng, G. D. , and Guo, X. , 1997, “ ε-Relaxed Approach in Structural Topology Optimization,” Struct. Optim., 13(4), pp. 258–266. [CrossRef]
Bruggi, M. , and Venini, P. , 2008, “ A Mixed FEM Approach to Stress-Constrained Topology Optimization,” Int. J. Numer. Methods Eng., 73(12), pp. 1693–1714. [CrossRef]
Le, C. , Norato, J. , Bruns, T. , Ha, C. , and Tortorelli, D. , 2010, “ Stress-Based Topology Optimization for Continua,” Struct. Multidiscip. Optim., 41(4), pp. 605–620. [CrossRef]
Holmberg, E. , Torstenfelt, B. , and Klarbring, A. , 2013, “ Stress Constrained Topology Optimization,” Struct. Multidiscip. Optim., 48(1), pp. 33–47. [CrossRef]
Hassani, B. , and Hinton, E. , 1998, “ A Review of Homogenization and Topology Optimization I—Homogenization Theory for Media With Periodic Structure,” Comput. Struct., 69(6), pp. 707–717. [CrossRef]
Czech, C. , 2012, “ Design of Meta-Materials Outside the Homogenization Limit Using Multiscale Analysis and Topology Optimization,” Ph.D. dissertation, Clemson University, Clemson, SC.
Czech, C. , Guarneri, P. , Thyagaraja, N. , and Fadel, G. , 2015, “ Systematic Design Optimization of the Metamaterial Shear Beam of a Nonpneumatic Wheel for Low Rolling Resistance,” ASME J. Mech. Des., 137(4), p. 041404.
Gonella, S. , and Ruzzene, M. , 2008, “ Homogenization and Equivalent In-Plane Properties of Two-Dimensional Periodic Lattices,” Int. J. Solids Struct., 45(10), pp. 2897–2915. [CrossRef]
Diaz, A. R. , and Bénard, A. , 2003, “ Designing Materials With Prescribed Elastic Properties Using Polygonal Cells,” Int. J. Numer. Methods Eng., 57(3), pp. 301–314. [CrossRef]
Lipperman, F. , Fuchs, M. B. , and Ryvkin, M. , 2008, “ Stress Localization and Strength Optimization of Frame Material With Periodic Microstructure,” Comput. Methods Appl. Mech. Eng., 197(45–48), pp. 4016–4026. [CrossRef]
Wang, H. V. , 2005, “ A Unit Cell Approach for Lightweight Structure and Compliant Mechanism,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
Joo, J. , and Kota, S. , 2004, “ Topological Synthesis of Compliant Mechanisms Using Nonlinear Beam Elements,” Mech. Based Des. Struct. Mach., 32(1), pp. 17–38.
Dangeti, V. S. , 2014, “ Identifying Target Properties for the Design of Meta-Material Tank Track Pads,” Igarss, Master's thesis, Clemson University, Clemson, SC.
Lundstedt, T. , Seifert, E. , Abramo, L. , Thelin, B. , Nyström, Å. , Pettersen, J. , and Bergman, R. , 1998, “ Experimental Design and Optimization,” Chemom. Intell. Lab. Syst., 42(1–2), pp. 3–40.
Merriam, E. G. , Jones, J. E. , and Howell, L. L. , 2014, “ Design of 3D-Printed Titanium Compliant Mechanisms,” 42nd Aerospace Mechanisms Symposium, Greenbelt, MD, May 14–16, pp. 169–174.

Figures

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Fig. 1

Schematic of the unit cell synthesis method for metamaterial design

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Fig. 2

EFGs and their general behavior (zeroth-order connection configuration)

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Fig. 3

First-order connection configuration

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Fig. 4

Second-order connection configuration

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Fig. 5

Metamaterial with uniaxial loading (left) and after deformation (right)

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Fig. 6

Stress–strain curve of SBR under uniaxial compression

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Fig. 7

FFB assembled with potential ESG to apply load and boundary conditions

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Fig. 8

Assembled EFG and ESG with periodicity for brick design

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Fig. 9

Design variables in the brick unit cell

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Fig. 10

Assembled brick design in 3 × 4 array

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Fig. 11

Parametric study of the brick design (1: High Value, 0: Low Value)

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Fig. 12

BrickOval unit cell with elemental geometries and parameters

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Fig. 13

Assembled BrickOval design in 3 × 4 array

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Fig. 14

Optimized BrickOval—target properties comparison

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Fig. 15

Cantilever unit cell with elemental geometries and design variables

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Fig. 16

Assembled cantilever design in 3 × 6 array

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Fig. 17

Parametric study of cantilever design (1: High Value, 0: Low Value)

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Fig. 18

CantiOval unit cell with elemental geometries and design variables

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Fig. 19

Optimized CantiOval—target properties comparison

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Fig. 20

Optimized CantiOval metamaterial

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Fig. 21

Force–displacement response of FFB with parameter sensitivities

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Fig. 22

Force–displacement response of Cantilever beam with parameter sensitivities

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Fig. 23

Force–displacement response of Oval-1 beam with parameter sensitivities

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Fig. 24

Force–displacement response of Oval-2 beam with parameter sensitivities

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