An evaluation of MPM, GIMP and CMPM in geotechnical problems considering large deformations

Abstract

Stress oscillations are a common phenomenon in the material point method (MPM), since this numerical method typically uses regular finite element (FE) shape functions to map variables from surrounding nodes to material points and vice versa, independently of the locations of the material points within an element. In integration this leads to a quadrature rule error and, in strain and stress calculations, derivatives of typical FE shape functions are discontinuous across element boundaries and do not give accurate results away from Gauss point locations within elements. In geotechnical analysis, the constitutive behaviour is generally stress-dependent, and therefore stress oscillations can cause severe inaccuracies in the calculated mechanical behaviour, including the development of wrong elasto-plastic quantities. Several attempts to improve stress recovery and reduce quadrature errors have been developed, but seldom has a full comparison between methods been made. In this paper, benchmark small scale and slope stability problems have been examined in order to compare the relative performance of the classic material point method (MPM), the generalized interpolation
material point (GIMP) method and the new compound material point method (CMPM)