Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation

Abstract

Soft cellular mechanical metamaterials (CMMs) have gained increasing attention due to their unique mechanical properties, especially when under large deformation. However, the strong nonlinearities and complex instabilities brought by the large deformation field is a critical challenge for the rational design of soft CMMs. In this work, we propose a mapped shape optimization method as a computational framework for inverse designs of soft CMMs.The core of this method is to introduce a fixed referential configuration. The geometric changes of the cellular structures are reflected by altering a differentiable shape map; and the deformation of the corresponding structures are determined by mapping the finite element computations to the referential configuration. Such formulation avoids the need to alter the background mesh and more importantly, provides an efficient way to compute the gradient of the objective functions with respect to the design variables via the adjoint method. The proposed method is of general purpose, and three distinct yet representative numerical examples are used to demonstrate the effectiveness of the method: optimizing unique overall mechanical properties, precise control of the onset of instability, and optimizing phononic band gaps. These examples cover a broad range of important engineering applications of soft CMMs.

Ultrafast Shape‐Reconfigurable Chiral Mechanical Metamaterial based on Prestressed Bistable Shells

“…Phononic structures can exhibit a range in frequency (named phononic band gaps) where the propagation of waves can be significantly attenuated. [47,48] The design of the phononic structures with such phononic band gaps has attracted great interest in recent years due to their potential as frequency modulators, [49] vibration isolators, [50] sound filters [51] and noise controllers. [52,53] We have illustrated the significant shapereconfiguration and tunable geometries of our proposed metamaterials, which enable the further exploration of tunable phononic band gaps that depend highly on structure geometries.…”

Inverse design of nonlinear mechanical metamaterials via video denoising diffusion models

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