A Thermodynamically Consistent Phase Field Framework for Anisotropic Damage Propagation

Abstract

In the present work, a thermodynamically consistent damage phase field formulation is adapted to include the effect of preferential directions in the damage evolution. A scalar damage variable is associated with each predefined preferential direction of crack propagation. Any other direction is penalized by a parameter $(\beta \gg 1)$ that represents the degree of anisotropy of the fracture. When $\beta =0$, the isotropic case is recovered. When there is more than one preferential direction, the material is considered totally fractured when any of the damage variables reaches value one. Simulations using the developed model show that it can reproduce the expected crack propagation pattern for materials with one and two preferential directions. In particular, the model was successful in simulating a zigzag crack pattern commonly obtained in double cantilever beam of spinel $MgA{l}_2{O}_4$ crystals. The model is fully dynamic in the sense that describes the actual time evolution of the unknown variables, in particular of damage growth. Moreover, anisotropic mechanical response can be easily included in the model by modifying the elasticity tensor.

Keywords:
Phase field models; Damage; Anisotropy; Finite element method

Graphical Abstract