A new efficient methodology for the analysis of mechanical metamaterials with elastic instabilities

Abstract

This work addresses the analysis of mechanical metamaterials exhibiting, as a distinguishing feature, snap-through instabilities in the elastic regime. Among the various opportunities offered by this feature is the manipulation of the material deformation energy [1] that allows the conception of reusable energy-trapping or energy-dissipation devices [2]. As a task to reach this objective, we present a novel computational methodology for analysing microarchitectures displaying elastic snap-through instabilities. The strategy is based on the construction of a surrogate model that reduces the computational burden if compared with full high-fidelity models of non-linear volumetric finite elements or with nonlinear beam elements. The surrogate model opens the possibility to analyse a large number of unit cells of periodic metamaterials with instabilities. In addition, it permits an efficient assessment of different geometrical configurations proving a suitable tool for its use in microarchitecture topology optimization processes. Noting that, in general, existing designs of this class of metamaterials only achieve energy manipulation in a specific predefined loading direction, in this work, and based on the proposed computational technique, we aim at the analysis of reusable multidirectional isotropic energy manipulation. This objective agrees with more realistic uses of metamaterials in which general boundary conditions, typically the loading directions, are not established a priori.