Optimal structures for failure resistance under impact

The complex physics and numerous failure modes of structural impact creates challenges when designing for resistance. While simple geometries layered material are conventional, advances in 3D printing additive manufacturing techniques have now made tailored or integrated multi-material structures achievable. Here, we apply gradient-based topology optimization to the design such structures. We start by constructing a variational model an elastic–plastic enriched with gradient phase-field damage, present novel method efficiently compute its transient dynamic time evolution. consider finite element discretization explicit updates displacements. damage field is solved through augmented Lagrangian formulation, splitting operator coupling between nonlinearity non-locality. Sensitivities over this trajectory computed adjoint method, develop numerical solve resulting dynamical system. demonstrate formulation studying optimal 2D solid–void undergoing blast loading. Then, explore trade-offs strength toughness spall-resistant structure composed two materials differing properties impact.