PFEM Modeling of Strain Localization Processes in Non-local Multiplicative Plasticity

A fully non-linear PFEM platform developed for coupled flow and deformation processes in saturated structured soils is employed in this work to explore the possibility of modeling the occurrence of strain localization and the evolution of the displacement field in the post-localization regime without the pathological mesh-dependence typically observed in conventional non-linear FEM simulation. The proposed formulation adopts an isotropic hardening elastoplastic model for bonded geomaterials, developed in the framework of multiplicative plasticity, equipped with non-local hardening laws of the integral type for both density- and bonding-related internal variables. These hardening laws provide the material with an internal length scale based on the size of the neighborhood where the non-local averaging is performed. A number of PFEM simulations of plane strain compression tests on ideal calcarenite specimens have been performed to explore the convergence of the numerical solution in the post-localization regime as the element size is reduced. The convergence study is focused on simulations with non-uniform, adaptive discretizations, exploring the convergence of the solution as the adopted minimum element size of the mesh is reduced. The results of the convergence study demonstrate the effectiveness of the adopted non-local approach in eliminating the pathological mesh-dependence in presence of strain localization, in the context of h-adaptive PFEM simulations.