Failure mitigation in optimal topology design using a coupled nonlinear continuum damage model

• Topology optimization of structures that account for damage localization is proposed.
• The algorithm concurrently couples topology optimization with nonlocal continuum damage mechanics.
• Damage constraints are introduced into the optimization description.
• We derive a path-dependent coupled adjoint formula for computing sensitivities.
• Optimized structures show increased resilience to failure caused by damage.

This paper presents a novel framework for performing topology optimization of structures while accounting for material damage. A quasi-static non-local brittle damage model is coupled to a linear finite element analysis code for modeling the structural response and the initiation and propagation of damage. The optimization problem is parameterized using SIMP variables, and failure mitigation is achieved through the enforcement of constraints on the maximum local damage intensity. We derive a computationally efficient adjoint sensitivity formulation that accounts for the path-dependence of the coupled analysis problem. The algorithm is validated through a series of numerical examples.