TOTAL LAGRANGIAN MATERIAL POINT METHOD FOR THE DYNAMIC ANALYSIS OF NEARLY INCOMPRESSIBLE SOFT MATERIALS

The material point method (MPM) shows good performance in modeling nonlinear dynamic problems and has been widely used to simulate various types of large deformation dynamic problems. However, the classical MPM may suffer from the volumetric locking when modeling the dynamic responses of the incompressible or nearly incompressible materials, which reduces the computational accuracy and affects the convergence behavior greatly. In this work, a displacement-pressure mixed total Lagrangian material point method (TLMPM) with explicit time integration is proposed for the large deformation dynamic behavior of nearly incompressible soft materials. In this method, an equation about the hydrostatic pressure is introduced based on the volumetric part of the strain energy density of nearly incompressible soft materials. Then the introduced equation as well as the momentum equation is discretized within the framework of the explicit MPM and the total Lagrangian formulation is implemented to overcome the cell-crossing noise, which increases the computational accuracy for the problems involving large deformation. Furthermore, the B-spline interpolation functions with different orders are applied for displacement and pressure fields respectively and the mixed TLMPM is improved to increase the accuracy by introducing a remapping technique for the volumetric deformation. In addition, the staggered solving scheme is adopted and the displacement and the pressure are required to be solved sequentially in a single time step. Finally, several typical numerical examples are simulated by the mixed TLMPM and the convergence and accuracy are analyzed. The results demonstrate that the proposed mixed TLMPM is able to deal with the volumetric locking effectively and simulate the dynamic behavior of nearly incompressible soft materials involving large deformation accurately.