Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM. The two methods are presented so as to highlight the similarities to rather than the differences from "standard" Updated Lagrangian (UL) approaches commonly employed by the Finite Elements (FE) community. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The vast majority of MPM techniques in the literatrue are based on some sort of explicit time integration. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields.
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