Asymptotic homogenization for phase field fracture of heterogeneous materials and application to toughening

Abstract

We propose an asymptotic homogenization framework to simulate the fracture of heterogeneous materials. This framework upscales the phase field model for microscale fracture and yields anisotropic effective properties such as the degraded elasticity tensor and the fracture toughness. Furthermore, it quantitatively accounts for the toughening effect in a simple way. More specifically, when the critical energy release rate of a heterogeneous material is uniform, the framework reveals that toughening is essentially determined by the disparity in the moduli of toughness, the energy per unit volume absorbed by the constituents before cracking.