Machine Learning-Guided Design of Non-Reciprocal and Asymmetric Elastic Chiral Metamaterials

TL;DR

This work addresses designing passive chiral metamaterials that simultaneously exhibit non-reciprocal and elastic asymmetric responses. It introduces design spaces defined by ligament geometry, contact angles, and circle radius, and employs Bayesian optimization with ensemble MLP surrogates to discover Pareto-optimal designs across eight non-reciprocity and eight asymmetry objectives. The study reveals that multiple contact states under loading drive extreme non-reciprocity and asymmetry, demonstrated through single- and multi-objective optimizations and Pareto front analyses. The findings establish a ML-guided pathway to programmable metamaterials capable of directed mechanical energy and novel wave phenomena, with broader implications for non-Hermitian and unidirectional wave control in passive systems.

Abstract

There has been significant recent interest in the mechanics community to design structures that can either violate reciprocity, or exhibit elastic asymmetry or odd elasticity. While these properties are highly desirable to enable mechanical metamaterials to exhibit novel wave propagation phenomena, it remains an open question as to how to design passive structures that exhibit both significant non-reciprocity and elastic asymmetry. In this paper, we first define several design spaces for chiral metamaterials leveraging specific design parameters, including the ligament contact angles, the ligament shape, and circle radius. Having defined the design spaces, we then leverage machine learning approaches, and specifically Bayesian optimization, to determine optimally performing designs within each design space satisfying maximal non-reciprocity or stiffness asymmetry. Finally, we perform multi-objective optimization by determining the Pareto optimum and find chiral metamaterials that simultaneously exhibit high non-reciprocity and stiffness asymmetry. Our analysis of the underlying mechanisms reveals that chiral metamaterials that can display multiple different contact states under loading in different directions are able to simultaneously exhibit both high non-reciprocity and stiffness asymmetry. Overall, this work demonstrates the effectiveness of employing ML to bring insights to a novel domain with limited prior information, and more generally will pave the way for metamaterials with unique properties and functionality in directing and guiding mechanical wave energy.

Figures (25)

• Figure 1: Illustration of the chiral metamaterial in shaatJMPS2023. The ligament was tied to two rigid circles at the ends. The ligament shape was fixed and the contact angle was $60^0$ at both sides.
• Figure 2: Illustration of the chiral metamaterial undergoing displacement from four directions. The reaction force of the right rigid circles in the $x$ and $y$ directions are denoted as $F_x$ and $F_y$. The stiffness values are calculated using the formula $k_{ij} = F_i/u_j$ when $u_j$ is nonzero. A superscript "$+$" is added to the displacement and stiffness symbol when the displacement is positive, and "$-$" when the displacement is negative.
• Figure 3: Mechanical model of the chiral structure under compression and extension. (a) Chiral structure under (i) compression load and (ii) extension load. The contact area of the deformed structure is highlighted with red color. (b) Equivalent mechanical model illustrating the contact mechanism with roller supporters substituting the contact area. (c) Distribution of Bending Moment and Axial Force along the beam.
• Figure 4: Bending and Stretching Energy distribution along the elastic ligament. (a) The schematic of the chiral structure. The design has a smaller stiffness $k_{xx}^-$ under compression loads, and a larger stiffness $k_{xx}^+$ under extension loads. (b) The bending and stretching distribution along the ligament under compression load. (c) The bending and stretching distribution along the ligament under extension load. The three figures (a)(b)(c) share the same x coordinates.
• Figure 5: Illustration of Pareto front for the multi-objective optimization of chiral metamaterial.