A Displacement-Volumetric Strain Mixed MPM for Incompressible Solid Analysis

Key Points

• The main goal is to develop a mixed formulation that addresses volumetric locking in the analysis of incompressible materials using the Material Point Method (MPM).
• Development of a mixed formulation incorporating displacement and volumetric strain for nodes.
• Use of the momentum conservation equation and volumetric strain rate definitions effectively.
• Introduction of stabilization terms to mitigate instabilities in single-step solutions.
• The new formulation shows reduced volumetric locking effects compared to the B-bar method.
• Smooth pressure distributions were achieved with appropriate stabilization parameters.
• Performance improvements were evidenced through multiple example calculations.