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

Abstract

SUMMARY 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.

A micropolar shell model for hard-magnetic soft materials

“…Next, the linearized equations resulting from Eqs. ( 31), (39), and ( 46) may be written as ∆δU e − ∆δW e = −(δU e − δW e ), (49) from which the following system of algebraic equations is extracted:…”

“…In this theory, each material particle is associated with a micro-structure that can undergo rigid rotations independently from its surrounding medium. Formulations of the micropolar theory to model localized elastic-plastic deformations (e.g., [44][45][46][47][48][49][50]) and size-dependent elastic deformations (e.g., [51][52][53][54][55][56]) have been developed. Some formulations to model micropolar shells have been also proposed (e.g., [57][58][59]).…”

Thermomechanics of Cosserat medium: modeling adiabatic shear bands in metals

“…The Cosserat theory finds many applications in geomechanics, because the mechanical behavior of the soil, being a granular material at macroscopic level, is characterized by a size effects already at macroscopic level [37,50,43]. However, besides geomechanics, the Cosserat model has also been extensively used both for homogeneous metal materials [22,4] and polycrystal materials [18,38,3,27], and many authors focused on different aspects of the Cosserat medium description. Steinmann and Willam investigated on the localization properties of the Cosserat model in elasto-plastic materials under infinitesimal deformations in case the loss of ellipticity was caused by negative material tangent operator [47].…”

“…Khoei et al drew a distinction between torsional and bending characteristic lengths, and they investigated the effect of these lengths on the shear bandwidth during different localization processes [29]. Many lines of work can also be found in literature proposing a thermodynamically-consistent model of the Cosserat kinematics [22,4,19,20,43].…”

Low-order mixed finite element analysis of progressive failure in pressure-dependent materials within the framework of the Cosserat continuum

“…In the past decades, various problems of progressive localization of strain have been tackled using the Cosserat continuum model. Representative works include, but are not limited to, Muhlhaus (1989); Muhlhaus and Vardoulakis (1987); de Borst (1991); de Borst and Sluys (1991); de Borst (1993); Steinmann (1994; 1995); Iordache and Willam (1998); Ehlers and Volk (1998); Ebrahimian et al (2012); Bauer et al (2012); Huang et al (2014); Huang and Xu (2015). In geomechanics, Li and Tang (2005), Tang and Li (2007), Tang et al (2013) developed a consistent algorithm for handling problems involving pressure-dependent elastoplastic materials in the framework of Cosserat continuum theory, in which a closed form of the consistent elastoplastic tangent modulus matrix was derived, and the resulting algorithm was applied for modelling strain localization phenomena because of strain-softening.…”