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In this paper we derive a novel fourth order gauge-invariant phenomenologicalmodel of infinitesimal rate-independent gradient plasticity with isotropichardening and Kr\"oner's incompatibility tensor $inc(\epsilon_p):= Curl[(Curl\epsilon_p)^T]$, where $\epsilon_p=sym p$ is the symmetric infinitesimalplastic strain tensor and $p$ is the (non-symmetric) infinitesimal plasticdistortion. Here, gauge-invariance denotes invariance under diffeomorphicreparametrizations of the reference configuration, suitably adapted to thegeometrically linear setting. The model features a defect energy contributionwhich is quadratic in the tensor $inc(\epsilon_p)$ and it contains isotropichardening based on the rate of the symmetric infinitesimal plastic straintensor $\dot{\epsilon_p}$. We motivate the new model by introducing a novelrotational invariance requirement in gradient plasticity, which we callmicro-randomness, suitable for the description of polycrystalline aggregates ona mesoscopic scale and not coinciding with classical isotropy requirements.This new condition effectively reduces the increments of the non-symmetricinfinitesimal plastic distortion $\dot{p}$ to their symmetric counterpart$\dot{\epsilon_p}$. In the polycrystalline case, this condition is a statementabout insensitivity to arbitrary superposed grain rotations. We formulate amathematical existence result for a suitably regularized non-gauge-invariantmodel. The regularized model is rather invariant under reparametrizations ofthe reference configuration including infinitesimal conformal mappings.

A fourth order gauge-invariant gradient plasticity model for polycrystals based on Kr\"oner's incompatibility tensor

A fourth order gauge-invariant gradient plasticity model for polycrystals based on Kr\"oner's incompatibility tensor