Explicit phase-field total Lagrangian material point method for the dynamic fracture of hyperelastic materials

Abstract

An explicit phase-field total Lagrangian material point method (TLMPM) is proposed in this paper for the effective simulation of the dynamic fracture behavior of hyperelastic solids involving massive deformation. In this method, the phase-field model is introduced to describe the cracks and the governing equations for the dynamic fracture of hyperelastic materials are derived via the Lagrangian equation. The total Lagrangian discrete formulation with explicit time integration is then developed for the coupled displacement and phase fields within the framework of the material point method (MPM) to handle the massive deformation involving fracture. Considering the impact and collision of soft materials, an improved contact algorithm based on particles in the TLMPM is developed to deal with the contact and self-contact response. Furthermore, the staggered single-iteration scheme is implemented to effectively solve the coupling discrete displacement and phase field governing equations. Two representative examples are presented to demonstrate the mesh convergence and accuracy of the proposed method. Finally, the collision of rings, the compression of hyperelastic blocks and the impact of a metal ball on a soft membrane are simulated and analyzed to illustrate the good performance of the proposed phase-field TLMPM in dealing with the dynamic fracture of soft materials with contact and self-contact involving massive deformation.