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.
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