Restoring Mesh Independency in FEM-DEM Multi-scale Modelling of Strain Localization Using Second Gradient Regularization

Continuum media from classical mechanics cannot appropriately reproduce the evolution of materials exhibiting strong heterogeneities in the strain field, e.g. strain localization. Models without a microscale representation cannot properly reproduce the microscale mechanisms that trigger the strain localization, in addition, first gradient relations don’t present any length parameter in the formulation. This results in a model without a characteristic length that cannot exhibit any objective band width. In this paper, techniques to introduce an internal length will be enumerated. Microstuctured materials will be retained and in particular Second Gradient model will be exposed and used along with a FEMxDEM approach. Numerical results showing the abilities of the enriched model will conclude the text.