Thermoelasticity at finite strains with weak and strong discontinuities

Abstract

This paper presents a monolithic coupled formulation for finite strain thermoelasticity with weak and strong discontinuities. Thermal and mechanical properties can vary sharply across embedded interfaces where weak discontinuities are allowed to grow into strong discontinuities as the coupled nonlinear process evolves. Significant contributions in this work are: (i) variationally consistent coupling of multiple fields that have jumps across embedded interfaces, (ii) non-matching meshes with provision of different element types across interfaces, (iii) evolution of interfacial kinematics via embedding phenomenological models at the interfaces, and (iv) consistent linearization of the two-way coupled formulation leading to quadratic convergence of the method. The new Variational Multiscale Coupled Field (VMCF) formulation is developed by embedding Discontinuous Galerkin (DG) ideas in the Continuous Galerkin (CG) method within the context of the Variational Multiscale (VMS) framework. Starting from a thermomechanically coupled formulation over the elastic domain with Lagrange multipliers that couple fields along the interfaces, the Lagrange multipliers are eliminated by deriving analytical expressions for the multipliers via the interfacial fine-scale problems facilitated by the VMS framework. The derived terms for interfacial stabilization are a function of the residual of Euler–Lagrange equations along the interfaces. Stabilization tensors are functions of the evolving mechanical and thermal fields and are free of user-defined parameters. Several test cases are presented to illustrate the versatility and the range of applicability of the method.