Numerical modelling of thermomechanical solids with mechanically energetic (generalised) Kapitza interfaces

Interfaces within a solid can play a significant role in the overall response of the body. The influence of the interface increases as the scale of the problem decreases. Furthermore, the properties of the interface can differ significantly from those of the surrounding bulk. Such effects are described here using interface elasticity theory. The objective of this presentation is to detail the computational aspects of modelling thermomechanical solids with mechanically energetic interfaces. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations, and dissipation. A mechanically energetic interface does not possess a thermal structure, and thus lacks its own heat capacity, heat conduction and heat expansion coefficient. For a mechanically energetic interface within a thermomechanical solid, the jump of the normal heat flux across the interface is zero while a temperature jump is allowed. In this sense, a mechanically energetic interface can be understood as a generalised Kapitza interface. Therefore the concept of Kapitza thermal resistance is used to control the temperature jump across the interface. The equations governing the fully-nonlinear, transient problem are given. They are then solved using an efficient finite element scheme. Key features of mechanically energetic interfaces are elucidated via a series of three-dimensional numerical examples.