A THERMODYNAMICAL THEORY OF ELASTIC MATERIAL INTERFACES

A thermodynamical theory is developed for interfaces between three-dimensional continua. Postulated balances of linear and rotational momentum and of energy, together with an entropy-growth inequality involving three temperature fields, take account of the thermo-mechanical interaction of the interface with its environment. Some general results are obtained for bodies whose boundaries exhibit surface effects. Elastic interfaces are defined and consequences of the Clausius–Duhem inequality examined. Of particular interest are the relationship between interfacial stress and free energy, and the different heat-conduction inequalities corresponding to various constitutive forms for heat transfer into the interface from its exterior. A linearized theory is derived and used to pose the initial/boundary-value problem for bodies with material boundaries. A uniqueness theorem is proved. The thermal expansion of a body is considered within the linear theory and the variation of thermal expansion coefficients with sample size predicted.