Numerical evaluation of the effective conductivities of composites with interfacial weak and strong discontinuities

• Elaboration of a numerical approach to evaluate effective conductivities of periodic composites.
• Interfaces embedded exhibit both temperature and normal heat flux discontinuities.
• Size- and shape-dependencies of the effective conductivities are studied in detail.

In the present paper, a computational approach based on the extended finite element method (XFEM) and the level set method (LSM) is first elaborated to evaluate the effective conductivities of particle- and fiber-reinforced composites where interfaces may be arbitrarily shaped while exhibiting both weak and strong discontinuities. An improved Master-Slave method is presented to efficiently deal with the periodic boundary conditions imposed on a representative unit cell of a given composites. A benchmark problem, whose analytic solution and approximated effective conductivities can be derived by theoretical deduction, is designated and applied to test the validity and robustness of elaborated computational approach. In particular, all numerical results are shown to be in excellent agreement with the relevant analytical ones. With the aid of computational approach validated, size- and shape-dependent effective conductivities of particle- and fiber-reinforced composites are studied and discussed in detail. Numerical examples are given to illustrate some results.