Analytical results describing plane thermoelastic fields and effective thermal expansion under the assumption of temperature dependency

We apply complex variable methods to develop analytical solutions of the inhomogeneity problem in which an inhomogeneity is embedded in an infinite matrix subjected to remote uniform thermal loads. We assume a nonlinear thermoelastic constitutive relationship and study the corresponding thermoelastic field as well as the effective thermal expansion under the assumption of non-uniform thermal expansion. Numerical results reveal the significant effect of temperature-dependent properties on the distribution of thermoelastic fields. In addition, the magnitude of the effective thermal expansion is shown to have a linear relationship with a newly introduced parameter K, which indicates that the temperature dependency of the matrix should not be neglected under non-uniform thermal expansion.