Interfacial coupling across incompatible meshes in a monolithic finite-strain thermomechanical formulation

Abstract

A stabilized interface method is presented for monolithic coupling of thermomechanical fields across incompatible internal interfaces. Embedding Discontinuous Galerkin (DG) ideas in the Variational Multiscale (VMS) framework yields interface coupling terms that accommodate nonmatching discretizations across glued meshes. A unique feature of the method that emanates from fine-scale modeling facilitated by VMS is the derivation of analytical expressions for the Lagrange multipliers that enforce continuity of the fields across nonmatching meshes. This stabilized form is free of any user-defined parameters and renders itself to consistent linearization that leads to quadratic convergence of the method. The coupling terms at the interface also provide an avenue to employ various kinematic models for interfacial response in multi-constituent materials. An interfacial gap/crack function is introduced together with the conjugate traction vector to model discrete interfacial failure in multi-material applications. An algorithm for consistent implementation of interfacial models for tension, compression, and sliding friction across non-conforming meshes is presented. Test cases that employ 8-node hexahedra and 4-node tetrahedra are presented that highlight the generality of the method and validate its robustness for mathematically nonsmooth thermomechanical problems.