Localized Deformation Analysis of a 3D Micropolar Modified Cam-Clay Model

Abstract

In classical continuum constitutive models, the loss of ellipticity of the governing rate equilibrium equations entails localizing deformations and mesh sensitivity in finite element simulations. Extensions of such models, rooted in the micromorphic continuum, aim at remedying mesh sensitivity by introducing length scales into the constitutive formulation. The micropolar continuum constitutes a special case of the micromorphic continuum and is commonly employed for remedying mesh sensitivity accompanying shear band failure. However, localizing deformations in the micropolar continuum remains largely unexplored. This study aims to investigate the conditions for localizing deformations in the micropolar continuum and to highlight their implications for 2D and 3D finite element simulations. To this end, we propose a micropolar extension of the modified Cam-clay model formulated in a three-dimensional infinitesimal elastoplastic framework and establish its localization characteristics following a method recently presented for the classical Cauchy–Boltzmann continuum. Investigations at the constitutive level highlight the stabilizing effect of the micropolar extension, which is increased both by the presence of couple stresses as well as by increasing the Cosserat couple modulus. Simulations at the structural level exhibit good agreement with the results obtained at the constitutive level and indicate that the Cosserat couple modulus required for adequately regularizing the structural response depends on the level of modal dilatancy. Even though localized failure is commonly regarded to be restricted to opening modes, we find mesh-sensitive structural behavior also in cases where the expected maximum modal dilatancy is far from unity.