Exploring the landscape of nonlinear mechanical metamaterials

Nonlinearities have recently emerged as a powerful tool for designing mechanical metamaterials, as they lead to systems with a complex and programmable response. Currently, nonlinear responses have primarily been explored through traditional experimental techniques and standard single-solution numerical solvers. Here, we use an in silico continuation method to discover multiple configurations with associated different properties for a single loading parameter. We test the method on simple porous structures under compressive loading; as the load increases, we discover bifurcating families of stable and metastable states. Using this method we find structures that can switch between energy-releasing and energy-harvesting configurations, and structures that are geometrically hysteretic. Physical experiments are conducted to validate the results.