Quantum mechanics

Algorithm

Recursion (computer science)

Engineering

Poromechanics

Geotechnical engineering

Displacement (psychology)

Animation

Applied mathematics

Computer graphics (images)

Material point method

Computer science

Mathematical optimization

Interpolation (computer graphics)

Solver

Quasistatic process

Geology

Porosity

Physics

Finite element method

Psychology

Mathematics

Psychotherapist

Porous medium

Structural engineering

Computer Methods in Applied Mechanics and Engineering

The material point method (MPM) has been increasingly used for the simulation of large-deformation processes in fluid-infiltrated porous materials. For undrained poromechanical problems, however, standard MPMs are numerically unstable because they use low-order interpolation functions that violate the inf–sup stability condition. In this work, we develop stabilized MPM formulations for dynamic and quasi-static poromechanics that permit the use of standard low-order interpolation functions notwithstanding the drainage condition. For the stabilization of both dynamic and quasi-static formulations, we utilize the polynomial pressure projection method whereby a stabilization term is augmented to the balance of mass. The stabilization term can be implemented with both the original and generalized interpolation material point (GIMP) methods, and it is compatible with existing time-integration methods. Here we use fully-implicit methods for both dynamic and quasi-static poromechanical problems, aided by a block-preconditioned Newton–Krylov solver. The stabilized MPMs are verified and investigated through several numerical examples under dynamic and quasi-static conditions. Results show that the proposed MPM formulations allow standard low-order interpolation functions to be used for both the solid displacement and pore pressure fields of poromechanical formulations, from undrained to drained conditions, and from dynamic to quasi-static conditions.

Stabilized material point methods for coupled large deformation and fluid flow in porous materials