Total-Lagrangian MPM for porous media published in IJNME

A total-Lagrangian material point method for fast and stable hydromechanical modeling of porous media

Conventional updated-Lagrangian MPM can be slow and unstable for hydromechanical analysis of saturated porous media.

This collaborative work presents a semi-implicit total-Lagrangian MPM. The fractional step method separates pore pressure from the kinematic fields, and the semi-implicit scheme avoids the small time steps imposed by permeability and fluid compressibility. Because shape functions are evaluated only once in the reference configuration, cell-crossing instabilities disappear and the system matrices keep a fixed structure, which allows an efficient Cholesky factorization.

Benchmarks show large speed-ups over conventional approaches while keeping accuracy.