An Eulerian method for finite deformation anisotropic damage with application to high strain-rate problems

This paper is dedicated to establishing a thermodynamically compatible Eulerian theoretical framework for elastoplastic anisotropically damaging materials, that is applicable to high strain rate and strongly compressible problems. The proposed model comprises a system of thermodynamically compatible balance laws based upon hyperelastic-inelastic theory: the mechanical conservation laws are supplemented by kinematic evolution equations for material deformation gradients, which can be written in conservative form. The formulation is rotationally invariant and hyperbolic, with a determinable characteristic structure. An operator split approach is proposed for integrating the governing constitutive models for three-dimensional Cauchy problems, in conjunction with a ghost material numerical method to resolve internal Dirichlet boundaries. Such methods naturally allow the generation of new internal boundaries making them ideal for simulating fragmenting materials and macroscale fracture. A remarkable feature of the proposed approach is that the overall complexity compares favourably with that of the model for elastoplastic deformations only. The simulation of expanding ring and flyer plate experiments are chosen to demonstrate the effectiveness of the proposed approach.