A Quasi-Static Method for Large Deformation Problems in Geomechanics

The Finite Element Method (FEM) has become the standard tool for the analysis of a wide range of mechanical problems. However, the classical FEM is not well suited for the treatment of large deformation problems since excessive mesh distortions require remeshing. The Material Point Method (MPM) represents an approach in which material points moving through a fixed finite element grid are used to simulate large deformations. As the method makes use of moving material points, it can be classified as a meshfree method. With no mesh distortions, it is an ideal tool for the analysis of large deformation problems. All existing MPM codes found in literature are dynamic codes with explicit time integration and only recently implicit time integration. In this study, a quasi-static MPM is presented. The paper starts with the description of the quasi-static governing equations, the numerical discretisation and an explanation of calculation procedures. Afterwards, geotechnical boundary-value problems are considered.