Inverse design of mechanical metamaterial achieving a prescribed constitutive curve

Besides exhibiting excellent capabilities such as energy absorption, phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations. This is facilitated by switching between different patterns under deformation. However, the related inverse design problem is quite challenging, due to the lack of appropriate mathematical formulation and the convergence issue in the post-buckling analysis of intermediate designs. In this work, periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by eliminating the degrees of freedom (DOFs) in void regions. Furthermore, by exploring the Pareto frontiers between error and cost, an inverse design formulation is proposed for unit cells. This formulation aims to achieve a prescribed constitutive curve and is validated through numerical examples and experimental results. The design approach presented here can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties.