Smoothed Total Lagrangian Material Point Method for Dynamic Large Deformation Analysis of Soft Materials

ABSTRACT A smoothed total Lagrangian material point method (STLMPM) is developed in this study to effectively simulate dynamic problems involving large deformation in nearly incompressible soft materials. In this method, the governing equations are spatially discretized within the framework of the total Lagrangian material point method (TLMPM) and temporally discretized using an explicit time integration scheme. To address the issue of decreased computational accuracy of the material point method (MPM) near physical domain boundaries, a Gaussian kernel function with kernel correction is employed to establish the interpolation formulas between particles and the background grid. Furthermore, to mitigate volumetric locking caused by the nearly incompressible nature of soft materials, the F ‐bar method is further developed within the framework of TLMPM. The accuracy and efficiency of the proposed STLMPM are demonstrated by several representative numerical examples, and the simulation results are compared with analytical solutions and other numerical methods.