Linear anisothermal theory for a viscoelastic laminated composite

A homogeneous continuum model is presented to describe the dynamic behavior of a laminated medium, including the effects of temperature variations. On the basis of assumed two-term expansions of the displacements and the temperature increments across the thicknesses of the layers, the state of deformation and the temperature distribution in the composite are described by six fields, i. e., gross displacements, local deformations, gross temperatures and local temperature variations. Balance equations are derived for the stress resultants and the first moments of the stresses across the thicknesses of the layers, as well as for resultant heat fluxes and their moments. A set of constitutive equations is presented for a laminated medium composed of layers of two anisotropic thermoviscoelastic solids. The special cases of isotropic thermoviscoelastic layers, anisotropic thermoelastic layers, and isotropic thermoelastic layers are discussed briefly.