Ebobisse, François; Neff, Patrizio A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner’s incompatibility tensor. (English) Zbl 1446.74093 Math. Mech. Solids 25, No. 2, 129-159 (2020). Summary: 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 tensor \(\text{inc} (\varepsilon_p ) := \text{Curl} [(\text{Curl} \varepsilon_p )^{\text{T}}]\), where \(\varepsilon_p\) 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 tensor \(\text{inc} (\varepsilon_p)\) and it contains isotropic hardening based on the rate of the plastic strain tensor \(\dot{\varepsilon}_p\). 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 distortion \(\dot{p}\) to their symmetric counterpart \(\dot{\varepsilon}_p = \text{sym } \dot{p}\). 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. Cited in 7 Documents MSC: 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 74E15 Crystalline structure Keywords:gradient plasticity; geometrically necessary dislocations; variational inequality; defect energy; incompatibility tensor; Riemann-Christoffel tensor; dislocation density; gauge theory of dislocations; infinitesimal conformal mappings; isotropy PDFBibTeX XMLCite \textit{F. Ebobisse} and \textit{P. Neff}, Math. Mech. Solids 25, No. 2, 129--159 (2020; Zbl 1446.74093) Full Text: DOI arXiv References: [1] Fleck, NA, Hutchinson, JW. Strain gradient plasticity. Adv Appl Mech 1997; 33: 295-361. · Zbl 0894.73031 [2] Fleck, NA, Müller, GM, Ashby, MF, Hutchinson, JW. Strain gradient plasticity: Theory and experiment. Acta Metall Mater 1994; 42: 475-487. [3] Nix, WD, Gao, H. Indentation size effects in crystalline materials: A law for strain gradient plasticity. 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