A space–time gauge theory for dynamic plasticity: Non-linear micro-inertia and its consequences

Abstract

Exploiting the invariance of energy density under local translation in space–time, a gauge theoretic model is developed for dynamic viscoplasticity in polycrystalline solids. The invariance is preserved using minimally replaced space–time gauge covariant operators. Translation in time leads to a new definition of gauge covariant temporal derivative; hence the classical notion of velocity is modified. Using a space–time pseudo-Riemannian metric, we derive an evolution equation for the equivalent plastic strain, which is expressed via the compensating fields thus giving it a geometric meaning. Dissipative terms and some higher order temporal and spatial derivatives naturally appear in the model. Also established is a correspondence of the compensating field due to spatial translation with Kröner’s multiplicative decomposition of the deformation gradient. Using this framework, we explicate on the geometric interpretation of certain internal variables often used in classical viscoplasticity models. In order to assess how the theory performs, we carry out numerical simulations of uniaxial and 3D continuum viscoplasticity problems. We specifically explore the role of a nonlinear micro-inertia term in phenomena involving anomalous strain rate sensitivity, e.g. negative strain rate sensitivity, strain rate locking, and in possible oscillations in the stress–strain response.