On the limit behavior of lattice-type metamaterials with bi-stable mechanisms

Abstract

This paper explores 2D lattice-type metamaterials featuring bi-stable unit cells andpredefined symmetry configurations. Our investigation delves into the emergence of phasetransition patterns and probes the limit behavior of these lattice arrangements. We develop a macroscale generalized standard material model based on a quasi-convexified freeenergy framework and validate it through a specific lattice configuration—a 1D chain ofbi-stable elements—where the relaxed free energy is analytically derived.To assess the limit behavior of the analyzed lattices, we elucidate the connection between energy release and topology at the microscale. This insight aids in identifyinglattice configurations yielding high extrinsic energy dissipation density. We introduce theconcept of dissipation efficiency and quantify it across all examined lattices under differentloading conditions. Transverse loads prevail in the studied configurations and exhibit adetrimental effect by diminishing extrinsic energy dissipation during metamaterial phasetransitions. To facilitate a comprehensive numerical assessment of diverse lattice configurations, we employ a surrogate model of the bistable element. This approach enables an efficient evaluation of sampling volumes constituted by numerous unit cells.