Properties of a composite material with mixed imperfect contact conditions

We present an analytical solution of a mixed boundary value problem for an unbounded 2D doubly periodic domain which is a model of a composite material with mixed imperfect interface conditions. We find the effective conductivity of the composite material with mixed imperfect interface conditions, and also give numerical analysis of several of their properties such as temperature and flux

A heat conduction problem of 2D unbounded composites with imperfect contact conditions

We consider a steady-state heat conduction problem in 2D unbounded doubly periodic composite materials with temperature independent conductivities of their components. Imperfect contact conditions are assumed on the boundaries between the matrix and inclusions. By introducing complex potentials, the corresponding boundary value problem for the Laplace equation is transformed into a special R-linear boundary value problem for doubly periodic analytic functions. The method of functional equations is used for obtaining a solution. Thus, the R-linear boundary value problem is transformed into a system of functional equations which is analysed afterwards. A new improved algorithm for solving this system is proposed. It allows to compute the average property and reconstruct the temperature and the flux at an arbitrary point of the composite. Computational examples are presented

Effective conductivity of a composite material with stiff imperfect contact conditions

We present an analytic and numerical analysis of several properties of a composite material with stiff imperfect interface conditions. Spaces of functions are identified where we can guarantee existence and uniqueness of solutions. In particular, formulas for the temperature distribution and flux are exhibited. Numerical calculations of the material characteristics such as temperature, flux and the effective conductivity are also performed and interpreted

Analytical methods for heat conduction in composites

Analytical methods unifying the study of heat conduction in various type of composite materials are described. Analytical formulas for the effective (macroscopic) conductivity tensor are presented

A composite material with inextensible-membrane-type interface

We consider a model of a composite material with “inextensible membrane type” interface conditions. An analytic solution of a stationary heat conduction problem in an unbounded doubly periodic two-dimensional composite whose matrix and inclusions consist of isotropic temperature-dependent materials is given. In the case where the conductive properties of the inclusions are proportional to those of the matrix, the problem is transformed into a fully linear boundary value problem for doubly periodic analytic functions. The solution makes it possible to calculate the average properties over the unit cell and discuss the effective conductivity of the composite. We present numerical examples to indicate some peculiarities of the solution.publishe

Analytical methods for heat conduction in composites

Analytical methods unifying the study of heat conduction in various type of composite materials are described. Analytical formulas for the effective (macroscopic) conductivity tensor are presented