Stress inaccuracies (oscillations) are one of the main problems in the material point method (MPM), especially when advanced constitutive models are used. The origins of such oscillations are a combination of poor force and stiffness integration, stress recovery inaccuracies, and cell crossing problems. These are caused mainly by the use of shape function gradients and the use of material points for integration in MPM. The most common techniques developed to reduce stress oscillations consider adapting the shape function gradients so that they are continuous at the nodes. These techniques improve MPM, but problems remain, particularly in two and three dimensional cases. In this paper, the stress inaccuracies are investigated in detail, with particular reference to an implicit time integration scheme. Three modifications to MPM are implemented, and together these are able to remove almost all of the observed oscillations.
The material point method (MPM) shows promise for the simulation of large deformations in history-dependent materials such as soils. However, in general, it suffers from oscillations and inaccuracies due to its use of numerical integration and stress recovery at non-ideal locations. The development of a hydro-mechanical model, which does not suffer from oscillations is presented, including a number of benchmarks which prove its accuracy, robustness and numerical convergence. In this study, particular attention has been paid to the formulation of two-phase coupled material point method and the mitigation of volumetric locking caused numerical instability when using low-order finite elements for (nearly) incompressible problems. The numerical results show that the generalized interpolation material point (GIMP) method with selective reduced integration (SRI), patch recovery and composite material point method (CMPM) (named as GC-SRI-patch) is able to capture key processes such as pore pressure build-up and consolidation.
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