A Topology Optimization Framework for the Inverse Design of Nonlinear Mechanical Metamaterials

Mechanical metamaterials are hierarchical structures that can be designed to possess exotic properties such as auxeticity, tunable stiffness, and bistability by optimizing the geometry of their microscale unit cells. This work develops a computational framework in which an arbitrary set of homogenized stress–strain goal points is defined, and topology optimization is employed to synthesize a unit cell to achieve the desired response. The framework extends the current state‐of‐the‐art by incorporating highly nonlinear phenomena such as internal contact, snap‐through buckling, and bistability in a single approach to capture a wide range of mechanical responses without the need for generating datasets, tuning parameters, or possessing prior knowledge of the optimal solution. Unit cells are generated for three challenging nonlinear responses and their behavior is validated via mechanical testing. The framework will enable the generation of highly nonlinear unit cells for metamaterials in applications such as morphing structures, soft robotics, and energy absorbing materials.