Modeling and simulation fracture in brittle materials with anisotropic surface energy

BIN LI; DANIEL MILLÁN; CHRISTIAN PECO; IRENE ARIAS; MARINO ARROYO

Barcelona

Congreso; 11th World Congress on Computational Mechanics (WCCM 2014); 2014

Spanish Association for Numerical Methods in Engineering

Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for fracture in brittle materials with anisotropic surface energy, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations. The variational nature of this model suggests that the underlying crack-path selection principle is related to the maximum energy release rate criterion, and in fact, it has been shown through asymptotic analysis that cracks propagate obeying the configurational torque balance in a weakly anisotropic phase-field model. The proposed variational phase-field model provides a new tool to analyze fracture in brittle materials with anisotropic surface energy from the computational side and may be a starting point for the mathematical analysis of this problem. From a computational viewpoint, phase-field models appear as the best approach to investigate this complex problem where the crack orientation selection is so crucial.