A Phase-Field Method for Elastic Mechanics with Large Deformation

Boundary tracking is a challenging numerical problem for elastic mechanics problems with large deformation. In particular, when the boundary conditions rely on the boundary shape, iteration is required between tracking boundaries and solving the elasticity equations. Stability of this iteration brings additional difficulty for designing efficient numerical methods. In this work, we introduce phase-field variables to represent different elastic domains and track the movement of boundaries. Furthermore, boundary conditions relying on the boundary shape can also be easily applied with the phase-field variables. Second-order compact finite difference schemes are used to solve the coupled system on a square-mesh staggered grid. Our numerical results show that the phase-field method can be conveniently used to solve complex elastic mechanics problems accurately.