Objective modelling of failure processes in brittle materials
mesh dependence and regularisation in the material point method
José León González Acosta (TNO)
Miguel A. Mánica (National Autonomous University of Mexico)
Philip J. Vardon (TU Delft - Civil Engineering & Geosciences)
Michael A. Hicks (TU Delft - Civil Engineering & Geosciences)
Antonio Gens (Universitat Politécnica de Catalunya)
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Abstract
Much of our effort in numerical analysis within geotechnical engineering is devoted to evaluating the likelihood of failure in a given boundary value problem (BVP). However, certain problems occasionally require studying the post-failure behaviour of the mobilised soil mass and its resulting consequences. These large deformation analyses exceed the capabilities of conventional finite element formulations, requiring the use of specialised numerical techniques, such as the material point method (MPM), which can mitigate mesh distortion issues. However, since MPM is based on the same principles as the finite element method (FEM), it shares many of its limitations, including volumetric locking and the hourglass effect, as well as additional challenges, such as stress oscillations due to material points crossing element boundaries. Furthermore, when combined with a constitutive description exhibiting softening, MPM can lead to non-objective results with a pathological dependence on the adopted mesh and poor convergence properties. Within this context, the present work addresses the importance of regularisation in MPM for the objective simulation of localised deformations in the presence of brittle materials. A nonlocal approach was incorporated within an existing MPM framework and applied to the simulation of a number of simple BVPs with a softening material. As in conventional FEM simulations, results without regularisation showed a more brittle global response and larger strains and displacements as the element size was reduced. Furthermore, and particularly relevant for studying the consequences of a given collapse, run-out distances were shown to depend on the mesh resolution. On the other hand, regularised simulations exhibited consistent behaviour, with a global response and a configuration of localised deformations that were approximately independent of the employed mesh. However, it was demonstrated that stress oscillation issues must also be addressed when softening is considered to prevent numerical instabilities.