Rocco Lagioia | Searcharxiv

arXiv2021

A micropolar isotropic plasticity formulation for non associated flow rule and softening featuring multiple classical yield criteria. Part II -- FE integration and applications

A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral decomposition of the former, considerable benefits are achieved. The integration requires the solution of a single equation in a single unknown, which is a considerable improvement as compared to the system of seven or four equations required by other approaches available in the literature for the Cauchy medium. The scheme also allows for a very efficient treatment of the singularity which affects the apex of most of the existing yield and plastic potential surfaces. Moreover, no complications arise when some of the principal stresses coincide. The algorithm has been implemented in a proprietary Finite Element program, and used for the constitutive model proposed in part I of this paper. Numerical analyses have been conducted to simulate a biaxial compression test and a shallow strip footing resting on a Tresca, Mohr-Coulomb, Matsuoka-Nakai and Lade-Duncan soil. The benefits of the Cosserat continuum over the Cauchy/Maxwell medium are discussed considering mesh refinement, non-associated flow and softening behaviour.

math.NA↗

arXiv2021

A micropolar isotropic plasticity formulation for non-associated flow rule and softening featuring multiple classical yield criteria Part I -- Theory

The Cosserat continuum is used in this paper to regularize the ill-posed governing equations of the Cauchy/Maxwell continuum. Most available constitutive models adopt yield and plastic potential surfaces with a circular deviatoric section. This is a too crude an approximation which hinders the application of the Cosserat continuum into practice, particularly in the geotechnical domain. An elasto-plastic constitutive model for the linear formulation of the Cosserat continuum is here presented, which features non-associated flow and hardening/softening behaviour, whilst linear hyper-elasticity is adopted to reproduce the recoverable response. For the formulation of the yield and plastic potential functions, a definition of the \textit{equivalent von Mises stress} is used which is based on Hencky's interpretation of the von Mises criterion and also on the theory of representations. The dependency on the Lode's angle of both the yield and plastic potential functions is introduced through the adoption of a recently proposed \textit{Generalized classical} criterion, which rigorously defines most of the classical yield and failure criteria.

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