Interfacial continuity and discontinuity relations are needed in dealing with a variety of mechanical and physical phenomena in heterogeneous media. The present work consists of three parts. In the first part concerned with perfect interfaces, two orthogonal projection operators reflecting the interfacial continuity and discontinuity of the field variables of coupled mechanical and physical phenomena are introduced, and some coordinate-free interfacial relations involving the surface decomposition of a generic linear constitutive law are deduced. The second part is dedicated to the derivation of a general linear imperfect interface model for coupled multifield phenomena by applying asymptotic analysis to a 3D curved thin interphase perfectly bonded to its two neighboring phases, the interfacial operators and relations given in the first part being used directly so as to render the derivation more direct and to write the final interfacial jump relations in a unified and compact way. The general imperfect interface model obtained in the present work includes as special cases all the relevant linear ones reported in the literature. In the third part, the derived general imperfect interface model is particularized to thermal conduction, elasticity and piezoelectricity. The corresponding imperfect interface models are numerically implemented by using the extended finite element method (XFEM) and appropriate enrichment functions.

The analytical exact solutions to benchmark problems are proposed to test the accuracy and to perform the convergence analysis of the elaborated numerical procedure. Finally, the imperfect interface models and the XFEM-based numerical procedure proposed are applied to the homogenization of composites accounting for imperfect interfacial effects.

Main references :

• [1] Gu, S.T., He, Q.-C. (2011), Interfacial discontinuity relations for coupled multifield phenomena and their application to the modelling of thin interphases as imperfect interfaces. Journal of the Mechanics and Physics of Solids 59, 1413-1426.
• [2] Gu, S.T., Liu, J.T., He, Q.-C. (2014), Size-dependent effective elastic moduli of particulate composites with interfacial displacement and traction discontinuities. International Journal of Solids and Structures 51, 2283-2296.
• [3] Liu, J.T., He, B., Gu, S.T., He, Q.-C. (2018), Implementation of a physics-based general elastic imperfect interface model in the XFEM and LSM context. International Journal for Numerical Methods in Engineering 115, 1499-1525.