Fracture toughness and auxeticity in disordered metamaterials

Auxetic metamaterials are commonly thought to exhibit favorable mechanical properties, notably high-energy absorption. Here we investigate disordered metamaterials obtained from random beam networks by optimizing simultaneously auxeticity and the energy absorbed before fracture. By giving different weights to these optimization targets, we demonstrate that the optimal configurations are connected along a Pareto front where high auxeticity implies comparatively low-energy absorption and vice versa. We study the mechanical properties of the resulting metamaterials and characterize the different deformation modes obtained for distinct optimization targets. The simulation and optimization results are validated by comparison with the deformation behavior of additively manufactured samples. Our work provides an illustration of the potentials and limitations of multiobjective optimization in the design of disordered mechanical metamaterials.