Research Papers: Design Automation

Designing and Harnessing the Metastable States of a Modular Metastructure for Programmable Mechanical Properties Adaptation

[+] Author and Article Information
R. L. Harne

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: harne.3@osu.edu

Z. Wu, K. W. Wang

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 25, 2015; final manuscript received October 27, 2015; published online December 10, 2015. Assoc. Editor: James K. Guest.

J. Mech. Des 138(2), 021402 (Dec 10, 2015) (9 pages) Paper No: MD-15-1446; doi: 10.1115/1.4032093 History: Received June 25, 2015; Revised October 27, 2015

Recent studies on periodic metamaterial systems have shown that remarkable properties adaptivity and versatility are often the products of exploiting internal, coexisting metastable states. Motivated by this concept, this research develops and explores a local-global design framework wherein macroscopic system-level properties are sought according to a strategic periodic constituent composition and assembly. To this end and taking inspiration from recent insights in studies of multiphase composite materials and cytoskeletal actin networks, this study develops adaptable metastable modules that are assembled into modular metastructures, such that the latter are invested with synergistic features due to the strategic module development and integration. Using this approach, it is seen that modularity creates an accessible pathway to exploit metastable states for programmable metastructure adaptivity, including a near-continuous variation of mechanical properties or stable topologies and adjustable hysteresis. A model is developed to understand the source of the synergistic characteristics, and theoretical findings are found to be in good agreement with experimental results. Important design-based questions are raised regarding the modular metastructure concept, and a genetic algorithm (GA) routine is developed to elucidate the sensitivities of the properties variation with respect to the statistics amongst assembled module design variables. To obtain target multifunctionality and adaptivity, the routine discovers that particular degrees and types of modular heterogeneity are required. Future realizations of modular metastructures are discussed to illustrate the extensibility of the design concept and broad application base.

Copyright © 2016 by ASME
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Wagg, D. , Bond, I. , Weaver, P. , and Friswell, M. , 2007, Adaptive Structures: Engineering Applications, Wiley, Chichester, UK.
Shim, J. , Shan, S. , Košmrlj, A. , Kang, S. H. , Chen, E. R. , Weaver, J. C. , and Bertoldi, K. , 2013, “ Harnessing Instabilities for Design of Soft Reconfigurable Auxetic/Chiral Materials,” Soft Matter, 9(34), pp. 8198–8202. [CrossRef]
Schenk, M. , and Guest, S. D. , 2013, “ Geometry of Miura-Folded Metamaterials,” Proc. Natl. Acad. Sci., 110(9), pp. 3276–3281. [CrossRef]
Crivaro, A. , Sheridan, R. , Frecker, M. , Simpson, T. W. , and von Lockette, P. , 2014, “ Bistable Compliant Mechanisms Using Magneto Active Elastomer Actuation,” ASME Paper No. DETC2014-35007.
Nicolaou, Z. G. , and Motter, A. E. , 2012, “ Mechanical Metamaterials With Negative Compressibility Transitions,” Nat. Mater., 11(7), pp. 608–613. [CrossRef] [PubMed]
Celli, P. , and Gonella, S. , 2015, “ Tunable Directivity in Metamaterials With Reconfigurable Cell Symmetry,” Appl. Phys. Lett., 106(9), p. 091905. [CrossRef]
Fuchi, K. , Buskohl, P. R. , Joo, J. J. , Reich, G. W. , and Vaia, R. A. , 2015, “ Resonance Tuning of RF Devices Through Origami Folding,” 20th International Conference on Composite Materials, Copenhagen, Denmark, pp. 1–10.
Florijn, B. , Coulais, C. , and van Hecke, M. , 2014, “ Programmable Mechanical Metamaterials,” Phys. Rev. Lett., 113(17), p. 175503. [CrossRef] [PubMed]
Silverberg, J. L. , Na, J. H. , Evans, A. A. , Liu, B. , Hull, T. C. , Santangelo, C. D. , Lang, R. J. , and Hayward, R. C. , and Cohen, I. , 2015, “ Origami Structures With a Critical Transition to Bistability Arising From Hidden Degrees Of Freedom,” Nat. Mater., 14(4), pp. 389–393. [CrossRef] [PubMed]
Shan, S. , Kang, S. H. , Wang, P. , Qu, C. , Shian, S. , Chen, E. R. , and Bertoldi, K. , 2014, “ Harnessing Multiple Folding Mechanisms in Soft Periodic Structures for Tunable Control of Elastic Waves,” Adv. Funct. Mater. 24(31), pp. 4935–4942. [CrossRef]
Wang, P. , Casadei, F. , Shan, S. , Weaver, J. C. , and Bertoldi, K. , 2014, “ Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials,” Phys. Rev. Lett., 113(1), p. 014301. [CrossRef] [PubMed]
Kuder, I. K. , Arrieta, A. F. , Rathier, W. E. , and Ermanni, P. , 2013, “ Variable Stiffness Material and Structural Concepts for Morphing Applications,” Prog. Aerosp. Sci., 63, pp. 33–55. [CrossRef]
Dai, F. , Li, H. , and Du, S. , 2013, “ A Multi-Stable Lattice Structures and Its Snap-Through Behavior Among Multiple States,” Compos. Struct., 97, pp. 56–63. [CrossRef]
Daynes, S. , Trask, R. S. , and Weaver, P. M. , 2014, “ Bio-Inspired Structural Bistability Employing Elastomeric Origami for Morphing Applications,” Smart Mater. Struct., 23(12), p. 125011. [CrossRef]
Bowen, L. , Springsteen, K. , Feldstein, H. , Frecker, M. , Simpson, T. W. , and von Lockette, P. , 2015, “ Development and Validation of a Dynamic Model of Magneto-Active Elastomer Actuation of the Origami Waterbomb Base,” J. Mech. Robots, 7(1), p. 011010. [CrossRef]
Li, S. , and Wang, K. W. , 2015, “ Fluidic Origami With Embedded Pressure Dependent Multi-Stability: A Plant Inspired Innovation,” J. R. Soc. Interface, 12(111), p. 20150639. [CrossRef] [PubMed]
Wu, Z. , Harne, R. L. , and Wang, K. W. , 2015, “ Exploring a Modular Adaptive Metastructure Concept Inspired by Muscle's Cross-Bridge,” J. Intell. Mater. Syst. Struct., (online).
Lakes, R. S. , and Drugan, W. J. , 2002, “ Dramatically Stiffer Elastic Composite Materials Due to a Negative Stiffness Phase?,” J. Mech. Phys. Solids, 50(5), pp. 979–1009. [CrossRef]
Fritzen, F. , and Kochmann, D. M. , 2014, “ Material Instability-Induced Extreme Damping in Composites: A Computational Study,” Int. J. Solids Struct., 51, pp. 4101–4112. [CrossRef]
Caruel, M. , Allain, J. M. , and Truskinovsky, L. , 2013, “ Muscle as a Metamaterial Operating Near a Critical Point,” Phys. Rev. Lett., 110(24), p. 248103. [CrossRef] [PubMed]
Schenk, M. , and Guest, S. D. , 2014, “ On Zero Stiffness,” Proc. Inst. Mech. Eng., Part C, 228(10), pp. 1701–1714. [CrossRef]
Puglisi, G. , and Truskinovsky, L. , 2002, “ A Mechanism of Transformational Plasticity,” Continuum Mech. Thermodyn., 14(5), pp. 437–457. [CrossRef]
Holst, G. L. , Teichert, G. H. , and Jensen, B. D. , 2011, “ Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms,” ASME J. Mech. Des., 133(5), p. 051002. [CrossRef]
Chen, Y. H. , and Lan, C. C. , 2012, “ An Adjustable Constant-Force Mechanism for Adaptive End-Effector Operations,” ASME J. Mech. Des., 134(3), p. 031005. [CrossRef]
Kovacic, I. , and Brennan, M. J. , eds., 2011, The Duffing Equation: Nonlinear Oscillators and Their Behaviour, Wiley, Chichester, UK.
Barbarino, S. , Saavedra Flores, E. I. , Ajaj, R. M. , Dayyani, I. , and Friswell, M. I. , 2014, “ A Review on Shape Memory Alloys With Applications to Morphing Aircraft,” Smart Mater. Struct., 23(6), p. 063001. [CrossRef]
Kidambi, N. , Harne, R. L. , and Wang, K. W. , 2016, “ Adaptation of Energy Dissipation in a Mechanical Metastable Module Excited Near Resonance,” ASME J. Vib. Acoust., 138, p. 011001. [CrossRef]
Romeo, F. , Sigalov, G. , Bergman, L. A. , and Vakakis, A. F. , 2015, “ Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Numerical Study,” ASME J. Comput. Nonlinear Dyn., 10, p. 011007. [CrossRef]
Biggs, N. L. , 1979, “ The Roots of Combinatorics,” Hist. Math., 6(2), pp. 109–136. [CrossRef]
Antoniadis, I. , Chronopoulos, D. , Spitas, V. , and Koulocheris, D. , 2015, “ Hyper-Damping Peroperties of a Stiff and Stable Linear Oscillator With a Negative Stiffness Element,” J. Sound Vib., 346, pp. 37–52. [CrossRef]
Haupt, R. L. , and Haupt, S. E. , 1998, Practical Genetic Algorithms, Wiley, Hoboken, NJ.
Freund, R. J. , Wilson, W. J. , and Mohr, D. L. , 2010, Statistical Methods, Academic Press, Burlington, MA.
Schaeffer, M. , and Ruzzene, M. , 2015, “ Wave Propagation in Multistable Magneto-Elastic Lattices,” Int. J. Solids Struct., 56–57, pp. 78–95. [CrossRef]
Tipton, C. R. , Han, E. , and Mullin, T. , 2012, “ Magneto-Elastic Buckling of a Soft Cellular Solid,” Soft Matter, 8(26), pp. 6880–6883. [CrossRef]
Shan, S. , Kang, S. H. , Raney, J. R. , Wang, P. , Fang, L. , Candido, F. , Lewis, J. A. , and Bertoldi, K. , 2015, “ Multistable Architected Materials for Trapping Elastic Strain Energy,” Adv. Mater., 27(29), pp. 4296–4301. [CrossRef] [PubMed]
Rafsanjani, A. , Akbarzadeh, A. , and Pasini, D. , 2015, “ Snapping Mechanical Metamaterials Under Tension,” Adv. Mater., 27(39), pp. 5931–5935. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

(a) Model schematic of bistable spring (double-well potential energy profile) in series with positive stiffness spring acted upon by end displacement. (b) Illustration of reaction force F adaptation when a one metastable module of a multimodule metastructure transitions from one to another metastable state: the force is modified to F + ΔF while end displacement z is constant. (c) Schematic of experimental, mechanical metastable module. Dimensions are given in mm. (d) Schematic of multimodule metastructure assembly and experimental implementation. (e) Top view photograph of one experimental module and (f) a multimodule metastructure.

Grahic Jump Location
Fig. 2

Normalized experimental reaction force as end displacement is varied. From top to bottom panels, measurements of one module, and then of two-, four-, and six-module metastructures. Each curve is a metastable state.

Grahic Jump Location
Fig. 3

Theoretical predictions of normalized reaction force F as end displacement z is varied. From top to bottom panels, results for one module, and then of two-, four-, and six-module metastructures. Each curve is a metastable state.

Grahic Jump Location
Fig. 4

Experimental measurements. (a) Transitioning a six module metastructure from common initial to common final states via different orders of transitions. Light to dark line shading indicates increasing mean value of reaction force with respect to all trials. (b) Distinct hysteresis loops having common minimum and maximum global end displacements, but unique sets of metastable states throughout slow actuation cycles. (c) Distinct hysteresis loops having common starting end displacement but qualitatively distinct unloading paths due to different maximum end displacement. In (b) and (c), background gray curves are quasi-static reaction force measurements; thick curves (colored) show two cycles of data, indicating repeatability to the measurements; circles indicate starting points.

Grahic Jump Location
Fig. 5

In (a)–(c), the performance objective is equidistant spacing among stable equilibria of a given six-module metastructure. In (d)–(f), the objective is equally spaced reaction forces while the global end displacement is fixed. The left-most panels illustrate the performance objectives according to the particular mechanical properties shown as circle points on the full profiles. In (a)–(f), design variable statistics of all 100 individuals in the final generation produced by the GA. Shading from light to dark shows increasing fitness toward achieving the performance objective. (a) and (d) Range, (b) and (e) mean, and (c) and (f) mean difference among the ordered design variable values as plotted in terms of the bistable spring stiffness and bistable spring span.

Grahic Jump Location
Fig. 6

GA results for equidistant stable equilibria. Design variable statistics, showing triangles as the mean statistics for a given generation whereas circles are the statistics according to the best-fit individual of that generation. (a) The mean of the six bistable spring stiffnesses, (b) the mean of the six bistable spring spans, (c) the mean difference among the ordered values of bistable spring stiffness and the corresponding statistic in (d) for the bistable spring span.

Grahic Jump Location
Fig. 7

GA results for equally spaced reaction force levels. Design variable statistics, showing triangles as the mean statistics for a given generation whereas circles are the statistics according to the best-fit individual of that generation. (a) The mean of the six bistable spring stiffnesses, (b) the mean of the six bistable spring spans, (c) the mean difference among the ordered values of bistable spring stiffness and the corresponding statistic in (d) for the bistable spring span.

Grahic Jump Location
Fig. 8

Generation mean design variable statistics over the course of 50 evolutionary generations. Shading from light to dark shows increasing generation number. Results in (a) and (b) are for the six module metastructure while those in (c) and (d) are for the twelve module metastructure. In (a) and (c) are the design variable ranges, while (b) and (d) show the design variable means.



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