Micropolar hyper‐elastoplasticity: constitutive model,consistent linearization,and simulation of 3D scale effects

A computational model for micropolar hyperelastic‐based finite elastoplasticity that incorporates isotropic hardening is developed. The basic concepts of the non‐linear micropolar kinematic framework are reviewed, and a thermodynamically consistent constitutive model that features Neo‐Hooke‐type elasticity and generalized von Mises plasticity is described. The integration of the constitutive initial value problem is carried out by means of an elastic‐predictor/plastic‐corrector algorithm, which retains plastic incompressibility. The solution procedure is developed carefully and described in detail. The consistent material tangent is derived. The micropolar constitutive model is implemented in an implicit finite element framework. The numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented. The results of the finite element simulations demonstrate (i) that the methodology is capable of capturing the size effect in three‐dimensional elastoplastic solids in the finite strain regime, (ii) that the formulation possesses a regularizing effect in the presence of strain localization, and (iii) that asymptotically quadratic convergence rates of the Newton–Raphson procedure are achieved. Throughout this paper, effort is made to present the developments as a direct extension of standard finite deformation computational plasticity. Copyright © 2012 John Wiley & Sons, Ltd.