A space-time gauge theory for modeling ductile damage and its NOSB peridynamic implementation

Abstract

Local translational and scaling symmetries in space-time is exploited for modelling ductile damage in metals and alloys over wide ranges of strain rate and temperature. The invariant energy density corresponding to the ductile deformation is constructed through the gauge invariant curvature tensor by imposing the Weyl like condition. The energetics of the plastic deformation is brought in through the gauge compensating field emerged due to local translation. Invariance of the energy density under the local action of translation and scaling is preserved through minimally replaced space-time gauge covariant operators. Minimal replacement introduces two non-trivial gauge compensating fields pertaining to local translation and scaling. These are used to describe ductile damage, including plastic flow and micro-crack evolution in the material. A space-time pseudo-Riemannian metric is used to lay out the kinematics in a finite-deformation setting. Recognizing the available insights in classical theories of viscoplasticity, we also establish a correspondence of the gauge compensating field due to spatial translation with Kröner's multiplicative decomposition of the deformation gradient. Thermodynamically consistent coupling between viscoplasticity and ductile damage is ensured through an appropriate degradation function. Non-ordinary state-based (NOSB) peridynamics (PD) discretization of the model is used for numerical implementation. The model's viability is tested in reproducing a few experimentally known facts, viz., strain rate locking in the stress-strain response, whose origin is traced to a nonlinear microscopic inertia term arising out of the space-time translation symmetry. Finally, we solved 2D and axisymmetric deformation problems for qualitatively validating the model's viability. NOSB peridynamics axisymmetric formulation in finite deformation setup is also presented.