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.

提出了一种稳定的接口方法，用于跨不兼容内部接口的热机械场的整体耦合。在不连续的多尺度（VMS）框架中嵌入不连续的Galerkin（DG）思想会产生接口耦合项，这些项可以适应跨胶合网格的不匹配离散化。由VMS促进的精细建模产生的方法的独特之处在于，拉格朗日乘子的解析表达式的推导可以在不匹配的网格上实现场的连续性。这种稳定的形式不包含任何用户定义的参数，并且使其具有一致的线性化效果，从而导致该方法的二次收敛。界面处的耦合项也为采用多种运动学模型进行多成分材料的界面反应提供了途径。界面间隙/裂纹函数与共轭牵引力矢量一起引入，以建模多材料应用中的离散界面破坏。提出了一种用于在不合格网格上进行拉伸，压缩和滑动摩擦的界面模型的一致实现的算法。提出了使用8节点六面体和4节点四面体的测试案例，这些测试案例突出了该方法的通用性并验证了其在数学上不平滑的热机械问题的鲁棒性。