An optimization approach to design deformation patterns in perforated mechanical metamaterials using distributions of Poisson’s ratio-based unit cells

Two-dimensional metamaterials with patterns of perforations producing auxetic effects can exhibit variable and tailorable deformation mechanisms by varying the distributions of cells with different geometry parameters. The local homogenized Poisson’s ratio can be used as a way to establish as a link between local unit cell parameters and global deformations. We propose here a Poisson’s ratio-based unit cell distribution optimization method to design deformation patterns in a perforated structure. A plate-like structure with centresymmetric perforations is here divided into different regions with dissimilar unit cell topologies that possess different homogenized Poisson’s ratio values. All the unit cells belonging to the same region have equal geometry. A differential evolution (DE) algorithm is used to optimize the permutation and combination of the homogenized local Poisson’s ratios of the unit cells regions. A two-dimensional perforated structure that satisfies the required deformation pattern can be obtained by using the proposed method. Simulations and experiments show that the proposed approach can provide controllable shape changes of 2D perforated mechanical metamaterials under uniaxial tensile loading.