Coupled thermoelasticity in a composite half-space

The problem of fully coupled thermoelasticity in a composite half-space is considered where the composite has variations in its physical properties in one direction only. The resulting one-dimensional problem thus depends on the so-called microscale of the composite. Homogenization of the fully coupled theory provides the leading order system of coupled equations (independent of the microscale) together with the effective physical properties of the thermoelastic medium. In particular the effective coupling parameter δ is found and it is shown to exhibit rather interesting properties; for a range of volume fractions in two-phase composites it is shown that δ lies below the corresponding coupling parameter for a homogeneous material made up of either phase. Transient boundary value problems of the homogenized system are then solved and compared with the classical problem of a homogeneous half-space. The magnitude of resulting discontinuities in field variables and their derivatives are found and their dependence on the effective coupling parameter is exhibited