Topology Optimization of Brittle Composites for Optimizing Fracture Resistance Incorporating Phase Field Method with Strain Orthogonal Decompositions

A framework of the topology optimization incorporated with the phase field method considering the interfacial damage for optimizing the fracture resistance of inclusion-matrix composites is presented. The topology optimization was performed to redistribute the inclusion phase in order to reduce its volume while keeping the fracture resistance value of the initial design unchanged. The phase field method uses two scalar phase field variables: one is for the bulk crack and the other is for the interfacial crack. The decomposition of the strain tensor into compression and tension parts was incorporated into this phase field method to improve the mechanical behaviors of the materials. These compression and tension strain parts are orthogonal in the context of the inner product in which the tensor of elastic stiffness behaves as a metric. Moreover, in the simulation process, an investigation of the effects of the interfacial parameters on the numerical results was discussed. Through the obtained results, the method proposed is demonstrated to be accurate and efficient in eliminating spurious effects and singularity points on the behavior curves in the damage process.