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Perturbation analysis of the effective conductivity of a periodic composite. (English) Zbl 1451.74066

Summary: We consider the effective conductivity \(\lambda^{\text{eff}} \) of a periodic two-phase composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. Then we study the behavior of \(\lambda^{\text{eff}} \) upon perturbation of the shape of the inclusions, of the periodicity structure, and of the conductivity of each material.

MSC:

74E30 Composite and mixture properties
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
35J25 Boundary value problems for second-order elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
45A05 Linear integral equations
74M15 Contact in solid mechanics
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