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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.

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Figures

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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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