Apparent Tensorial Conductivity of Layered Composites
A lamination theory is proposed to treat a multilayered composite material as an anisotropic but homogeneous equivalent material. The conductivity tensor and the governing differential equations of the equivalent material are derived. A sample heat conduction problem for a laminated cylindrical body is solved by the present approach and results compared favorably with the exact solution. Nomenclature K = conductivity KLj — conductivity tensor qi = heat flux in the direction of x, Rij = resistivity tensor T — temperature V = volume fraction 4> = dimensionless temperature defined in Eq. (21) r\ = dimensionless temperature defined in Eq. (27) Sij = Kronecker delta Superscripts "p" = pth layer or component (") = dimensionless quantities defined in Eqs. (21) and (27).