Topology optimization of particle-matrix composites for optimal fracture resistance taking into account interfacial damage

This paper presents a topology optimization framework for optimizing the fracture resistance of two-phase composites considering interfacial damage interacting with crack propagation through a redistribution of the inclusions phase. A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of discontinuities. This formulation avoids the burden of remeshing problem during crack propagation and is well adapted to topology optimization purpose. Efficient design sensitivity analysis is performed by using the adjoint method, and the optimization problem is solved by an extended bidirectional evolutionary structural optimization method. The sensitivity formulation accounts for the whole fracturing process involving crack nucleation, propagation, and interaction, either from the interfaces and then through the solid phases, or the opposite. The spatial distribution of material phases are optimally designed using the extended bidirectional evolutionary structural optimization method to improve the fractural resistance. We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process.