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 and predefined symmetry configurations. Our investigation delves into the emergence of phase-transition patterns and probes the limit behavior of these lattice arrangements. We develop a macroscale generalized standard material model based on a quasi-convexified free energy framework and validate it through a specific lattice configuration—a 1D chain of bi-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 identifying lattice configurations yielding high extrinsic energy dissipation density. We introduce the concept of dissipation efficiency and quantify it across all examined lattices under different loading conditions. Transverse loads prevail in the studied configurations and exhibit a detrimental effect by diminishing extrinsic energy dissipation during metamaterial phase transitions. 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.