VARIATIONALLY DERIVED DISCONTINUOUS GALERKIN METHOD: APPLICATION TO DYNAMIC THERMOELASTICITY

Abstract

This paper presents a variational approach for deriving discontinuous Galerkin (DG) method for coupled field problems. Starting from the variational multiscale discontinuous Galerkin (VMDG) framework that is applied to the mechanical and thermal fields across embedded interfaces, an interface DG method for the coupled multifield problems is developed. Extending the interface DG to all inter-element boundaries naturally leads to a full DG method. An important aspect of the proposed methods is that time dependency appears naturally in the analytical expressions for the Lagrange multipliers that enforce the continuity of the fields and their fluxes. Unique attributes of the analytical expressions are that they comprise material and geometric parameters that automatically embed the concepts of stress averaging and area averaging in the method. In addition, the interface terms also provide an avenue to variationally account for interfacial kinetic and kinematic models for a robust representation of interfacial physics in dynamic thermomechanical problems. The interface DG method where discontinuity in the fields exists only at the embedded interfaces while continuous formulation is employed in the rest of the domain is well suited for bimaterial interface problems as well as for obtaining computationally economic solutions to the general class of mathematically nonsmooth thermomechanical problems. Several benchmark test cases are investigated that highlight the enhanced stability and variational consistency of the proposed VMDG formulations.