An XFEM-based numerical procedure for the analysis of poroelastic composites with coherent imperfect interface

Composites under consideration consist of a poroelastic matrix in which poroelastic inclusions are embedded via a poroelastic transition layer of small uniform thickness. A prototype of such poroelastic composites is concrete in which aggregates are often bonded to a cement paste through an interfacial transition zone (ITZ). In this work, the poroelastic transition layer is replaced by an interface of zero thickness described by the poroelastic coherent imperfect interface model. According to this model, the displacement and pore pressure are continuous across the interface but the traction and normal fluid flux suffer interfacial jumps. The main objective of this work is to propose an efficient numerical solution to the problem of poroelastic composites with coherent imperfect interface under the regime of undrained saturation. To this end, the weak formulations are first established for the relevant boundary value problems of linear poroelasticity and fluid transport. The extended finite element method (XFEM) and level-set method (LSM) are then used to elaborate a numerical procedure. The accuracy and convergence rate of this procedure are analyzed with the aid of a benchmark problem whose analytical exact solution is derived. The numerical procedure proposed turns out to be efficient in capturing the interfacial discontinuities and computing the elastic and transport fields, and can be applied, for example, to solving the important problem of homogenizing poroelastic composites with coherent imperfect interface.