Adaptive phase-field smoothed total Lagrangian material point method for fracture analysis of soft materials involving large deformation

Abstract

An adaptive phase-field smoothed total Lagrangian material point method (APS-TLMPM) is proposed in this paper to analyze the fracture behavior of nearly incompressible materials. The total Lagrangian material point method (TLMPM) combining with the phase-field model (PFM) is developed to describe the fracture behavior and solve the governing equations. Moreover, a hybrid F-bar method is developed to effectively alleviate volumetric locking caused by the nearly incompressible nature of soft materials. The physically meaningful and numerically induced volumetric changes are distinguished based on the pressure field to mitigate the inconsistency between the incompressibility constraint and the diffusive crack model. To efficiently solve the phase-field governing equations, an adaptive mesh refinement (AMR) algorithm is developed to refine the background grid and particles near the crack tip. Meanwhile, a unified formulation for constructing interpolation functions is established based on corrected smoothed kernel functions to efficiently handle transition grid with hanging nodes generated by the AMR. Finally, the accuracy and effectiveness of the proposed method for simulating the fracture of nearly incompressible materials are demonstrated through several representative numerical examples and comparisons with experimental results.