The strong and weak forms of a general imperfect interface model for linear coupled multifield phenomena

Imperfect interfaces are present in a variety of practical situations in mechanics and physics. In particular, they play an essential role in determination of mechanical and physical properties of composite materials. In a recent paper by Gu and He (2011), a general imperfect interface model for linear coupled multifield phenomena is rigorously derived which includes as special ones the widely used linear imperfect interface models proposed on the basis of some phenomenological considerations. The present paper aims at the establishment of the weak form for the boundary value problem of composites with general imperfect interfaces, which is the first key step towards numerically implementing the imperfect interface effects within the framework of finite element. To achieve this objective, firstly, the general imperfect interface model is reformulated in such a way that a particularly simple and compact strong form is obtained for it. Then, its weak form is derived in the general context of coupled multifield phenomena and expressed in a unified way for various linear mechanical and physical phenomena. Finally, the general results are particularized to transport phenomena, elasticity and piezoelectricity, together with detailed discussions on extreme situations in each case.