Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session V57: Mechanical Metamaterials IFocus

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Sponsoring Units: GSNP Chair: Sung Kang, Johns Hopkins University Room: BCEC 256 
Thursday, March 7, 2019 2:30PM  3:06PM 
V57.00001: Sequential Metamaterials Invited Speaker: Martin Van Hecke Ordered sequences of motion govern the morphological transitions of a wide variety of natural and manmade systems, while the ability to interpret timeordered signals underlies future smart materials that can be (re)programmed and process information. Here we introduce two types of mechanical metamaterials, that either exhibit sequential output or are sensitive to sequential input. 
Thursday, March 7, 2019 3:06PM  3:18PM 
V57.00002: Inverse Kirigami Design Gary Choi, Levi Dudte, L Mahadevan The basic building block of any kirigami pattern is a periodic planar motif with cuts that allow the unit cell to open or close via planar rotations. The tessellations of the plane can take many forms  quads, kagome lattices, and even Islamic tilings. Recent work has explored these geometries in the context of mechanical metamaterials, and focused primarily on the forward problem  given a topology and geometry of the kirigami pattern, how does it deploy and what are the mechanical properties of the structure. In this work, we pose and solve the inverse problem of designing the number, size, and orientation of cuts that allows us to convert a closed, compact regular kirigami tessellation of the plane into a deployment that conforms approximately to any prescribed target shape in two and three dimensions. 
Thursday, March 7, 2019 3:18PM  3:30PM 
V57.00003: Inverse design of mechanical metamaterials that harness instabilities Giorgio Oliveri, Johannes Overvelde Metamaterials derive their properties from their structure rather than their chemical composition. Their microstructure is specifically designed to create new functionalities not found in nature. Harnessing instabilities is a prominent practice of turning continuous deformations into a discrete response, allowing for sequential transformations, multistability and hysteretic behavior. Despite the complex behavior that these mechanical metamaterials show, their architecture is often surprisingly simple. An iconic example of auxetic material is an elastomeric material patterned with circular pores. While several studies focused on the effects of pore shape and pore distribution, the mechanical properties can only be tuned within limits set by a few geometrical parameters. Our aim is to reverse this paradigm. We introduce a stochastic topology optimization strategy, to inversely design mechanical metamaterials with targeted buckling behavior. Our study, while first focusing on optimizing structure with assigned buckling force, extends at designing structures with predefined postbuckling behavior. This opens up exciting opportunities for the design of soft robots where functionalities can be encoded in the material itself. We complement our results with experimental verification. 
Thursday, March 7, 2019 3:30PM  3:42PM 
V57.00004: Bayesian Optimization of Equilibrium States in Architected Elastomers David Yoo, carson Willey, Andrew Gillman, Vincent Chen, Abigail Juhl, Philip Buskohl Hyperelastic latticebased architectures have demonstrated potential for energy absorption and vibration control due to their inherent buckling instabilities, which reconfigure the energy and stiffness distribution of the structure. Multiresonant vibration isolation can possibly be achieved by tuning the local stiffness properties between the stable equilibrium states. In this study, we develop a design optimization framework to tune the local configuration of the stable equilibrium points and characterize the transition in stiffness through the bistability. We utilize Bayesian optimization to navigate the design space through a balanced approach of exploitation and exploration. The design architecture is parameterized with a Fourier series expansion of the beam geometry, which controls the periodicity and phase of the beam thickness as a function of length. The forcedisplacement relationship of each design candidate is calculated by the finite element method and segmentation of mono and bistable designs is employed to retain the desired behavior of the response surface. The preliminary results suggest the periodicity of the beam thickness, parameterized by the 1st term in Fourier series, most critically affects the bistability mode. 
Thursday, March 7, 2019 3:42PM  3:54PM 
V57.00005: Understanding the Effect of Torsion on Auxetic Behaviors of ThreeDimensional Networks Meng Shen, Nidhi Pashine, Sidney Robert Nagel, Juan De Pablo Bond pruning has recently proved to be an effective method for designing auxetic networks. Previous theoretical work on auxetic networks includes bond compression terms only, which is a reasonable analog for tenuous systems and frictionless granular packings. For networks made in the laboratory, however, our recent work has shown that the auxetic behavior depends not only on geometry, but also on the interaction parameters, in particular the angle bending term. In threedimensional networks, the torsion of local connected bonds provides an additional degree of freedom. Here we investigate the effect of torsion on the auxetic behavior of ordered and disordered 3D networks. The research provides insights for the design of 3D networks for the auxetic behavior. 
Thursday, March 7, 2019 3:54PM  4:06PM 
V57.00006: Elastic multipole method for describing deformation of 2D solid structures with circular holes and inclusions Siddhartha Sarkar, Matjaz Cebron, Miha Brojan, Andrej Kosmrlj The analogies between electrostatics and elasticity help us to solve complicated boundary value problems in linear elasticity of 2D solid structures. For example, a hole inside an elastic body is analogous to a perfect conductor in electrostatics in the sense that at the circumference of them the fields, namely the traction force and the parallel component of the electric field respectively, have to be zero. Similarly, an inclusion in an elastic material is equivalent to a dielectric since in both cases the fields have to be continuous at the edge of the inhomogeneity. Furthermore, just like external electric field induces polarization (dipoles, quadrupoles, etc.) of conductive objects, external stress induces elastic multipoles inside holes. Based on this idea, we present a method for obtaining deformations of 2D solid structures with circular holes and inclusions under applied load. We validated the method by comparing the results with tabletop experiments. We also utilized the method of image charges from electrostatics to capture the effect of boundaries on the deformed shapes of the holes/inclusions. The excellent agreement with the experimental results shows the power of this intuitive method. 
Thursday, March 7, 2019 4:06PM  4:18PM 
V57.00007: Homogenisation bounds for microarchitected polymer materials with extreme mechanical properties Filippo Matteo Agnelli, Andrei Constantinescu, Grigor Nika

Thursday, March 7, 2019 4:18PM  4:30PM 
V57.00008: Reconfigurable materials through chirped design Jiayi Wu, Nidhi Pashine, Leah Roth, Heinrich M Jaeger, Sidney Robert Nagel, Arvind Murugan Evolution in timevarying environments naturally leads to adaptable biological systems that can switch functionalities easily. Here we exploit this principle to design materials that can switch between two distinct functionalities with minimal changes in design parameters. We consider highdimensional materials design problems where any particular functionality can be effectively realized by numerous equivalent choices of design parameters. We run native design algorithms like gradient descent or CMAES for these problems; however, we switch the target functionality between two distinct targets at regular intervals, even if the design is incomplete. By systematically increasing the frequency of such switches in a `chirpâ€™, we naturally uncover pairs of parameter sets that exhibit the two target functionalities but are minimally different from each other. We apply these ideas to design mechanical networks that can switch deformation modes with minimal bond changes and to design 3d shapes that can switch between specified packing fractions with minimal shape changes. 
Thursday, March 7, 2019 4:30PM  4:42PM 
V57.00009: Domain Evolution Kinietics with Vector Order Parameter in Multistable Metamaterial Michael Frazier, Romik Khajehtourian, Dennis Kochmann Multistability characterizes a variety of physical systems across diverse disciplines from chemistry, to biology, to materials science, etc. Recently, metamaterials emerging from geometrically multistable architectures have attracted the interests of researchers for the elaborated mechanical and dynamic response. Within such systems, multiple opposing, energetically stable phases may exist simultaneously, separated by a domain walls. Under the appropriate conditions, domain walls move, a smallscale process whose influence, nonetheless, manifests at much larger scales. Ferroelectric switch and grain growth affecting piezoelectricity and strength of materials are two familiar examples from materials science. Previously, we simulated ferroelectriclike switching and solidificationlike phase separation in a multistable metamaterial for which the theoretical descriptions required only a scale order parameter. In this talk, we present a metamaterial design whose theoretical description of the domain evolution kinetics demands a vector order parameter. This additional complexity realizes many atomicscale features within a readily accessible, largescale platform which is of interest to materials scientist and mechanical engineers alike. 
Thursday, March 7, 2019 4:42PM  4:54PM 
V57.00010: Mechanical response of wrinkled structures Sijie Tong, Andrej Kosmrlj Surface wrinkling of compressed thin films on soft substrates has been of great interest both in fundamental studies and in practical applications. While the formation and evolution of wrinkled structures is well understood, much less is known about how wrinkled surfaces respond to external forces. In this talk, I will discuss how wrinkled structures respond to an infinitesimal point force. We find that the linear response diverges near the onset of the wrinkling instability and that it decays away from this critical threshold, where wrinkles are fully developed. Furthermore, we find that the dominant response comes from the Fourier modes that correspond to the wavelength of wrinkles. In analogy with the critical phenomena in ferromagnets, we can introduce critical exponents for the mechanical response of wrinkled structures, which are consistent with the Landau theory. Finally, I will also comment on how to use this theory to study the response of wrinkled structures to more complicated distributions of external forces, such as the interaction of wrinkled surfaces with liquid droplets. 
Thursday, March 7, 2019 4:54PM  5:06PM 
V57.00011: Mechanical failure of disordered networks derived from frictional packings. Estelle Berthier, Jonathan E Kollmer, Silke Henkes, Kuang Liu, Jennifer Schwarz, Karen Daniels Disordered networks are widely used to study heterogeneous material failure. These structures are inherent to many systems such as rigid foams or granular materials. In particular, the latter exhibit highly heterogeneous force chain networks that appear to control the response of such media to external perturbations. 
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