A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner's incompatibility tensor. (February 2020)

• Record Type: Journal Article
• Authors: Ebobisse, François; Neff, Patrizio
• Is Part Of: Mathematics and mechanics of solids. Volume 25:Number 2(2020)
• Page Start: 129
• Page End: 159
• Publication Date: 2020-02
• Subjects: gradient plasticity -- geometrically necessary dislocations -- variational inequality -- defect energy -- incompatibility tensor -- Riemann–Christoffel tensor -- dislocation density -- gauge theory of dislocations -- infinitesimal conformal mappings -- isotropy; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286519845026
• Languages: English
• ISSNs: 1081-2865

Abstract

In this paper we derive a novel fourth-order gauge-invariant phenomenological model of infinitesimal rate-independent gradient plasticity with isotropic hardening and Kröner's incompatibility tensorinc ( ε p ) : = Curl [ ( Curl ε p ) T ], whereε p is the symmetric plastic strain tensor. Here, gauge-invariance denotes invariance under diffeomorphic reparametrizations of the reference configuration, suitably adapted to the geometrically linear setting. The model features a defect energy contribution that is quadratic in the tensorinc ( ε p ) and it contains isotropic hardening based on the rate of the plastic strain tensorε · p . We motivate the new model by introducing a novel rotational invariance requirement in gradient plasticity, which we call micro-randomness, suitable for the description of polycrystalline aggregates on a mesoscopic scale and not coinciding with classical isotropy requirements. This new condition effectively reduces the increments of the non-symmetric plastic distortionp · to their symmetric counterpartε · p = sym p · . In the polycrystalline case, this condition is a statement about insensitivity to arbitrary superposed grain rotations. We formulate a mathematical existence result for a suitably regularized non-gauge-invariant model. The regularized model is rather invariant under reparametrizations of the reference configuration including infinitesimal conformal mappings.