A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media

摘要

An arbitrarily curved three-dimensional anisotropic thin interphase between two anisotropic solids is considered. The purpose of this study is to model this interphase as a surface between its two neighbouring media by means of appropriately devised interface conditions on it. The analysis is carried out in the setting of unsteady heat conduction and dynamic elasticity, and makes use of the simple idea of a Taylor expansion of the relevant fields in thin regions. It consists of a generalization of a previous study by Boevik [1994. On the modelling of thin interface layers in elastic and acoustic scattering problems. Q. J. Mech. Appl. Math. 47, 17—42] which was confined to the isotropic setting. The remarkable feature of the presently derived anisotropic interface model is that formally it has a more compact form than that of Boevik's isotropic version. This is achieved by a judicious choice of surface differential operators which have been used in the derivation, and makes possible to show that several previously known classical interface models are recovered as special cases of the one obtained in this study, once suitable assumptions are made on the magnitude of the conductivity and elasticity tensors of the interphase.