A thermomechanical anisotropic model for shock loading of elastic-plastic and elastic-viscoplastic materials with application to jointed rock

摘要

A large deformation thermomechanical model is developed for shock loading of a material that can exhibit elastic and inelastic anisotropy. Use is made of evolution equations for a triad of microstructural vectors which model elastic deformations and directions of anisotropy. Specific constitutive equations are presented for a material with orthotropic elastic response. The rate of inelasticity depends on an orthotropic yield function that can be used to model weak fault planes with failure in shear and which exhibits a smooth transition to isotropic response at high compression. Moreover, a robust, strongly objective numerical algorithm is proposed for both rate-independent and rate-dependent response. The predictions of the continuum model are examined by comparison with exact steady-state solutions. Also, the constitutive equations are used to obtain a simplified continuum model of jointed rock which is compared with high fidelity numerical solutions that model a persistent system of joints explicitly in the rock medium.