Inverse design of mechanical metamaterial achieving a prescribed constitutive curve

Besides showing excellent abilities such as energy absorption, phase-transforming metamaterials provide a rich design space for achieving nonlinear constitutive relations by switching between different patterns under deformation. The related inverse design problem, nevertheless, is quite challenging due to the lack of appropriate mathematical formulation and the convergence issue of post-buckling analysis of intermediate designs. In the present work, periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by removing the DOFs of void regions. Furthermore, exploring the Pareto frontiers between error and cost, an inverse design formulation is proposed for unit cells achieving a prescribed constitutive curve and validated by numerical examples and experimental results. The present design approach can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties.