Real-form solution for an anisotropic elastic elliptical inhomogeneity under uniform heat flux

We use the extended Stroh sextic formalism for thermo-anisotropic elasticity to present an elegant solution of the problem of an anisotropic elastic elliptical inhomogeneity embedded in an infinite anisotropic elastic matrix subjected to uniform remote heat flux. We prove rigorously that the remote thermal stresses cannot be set to zero in a generally anisotropic elastic matrix. In particular, a real-form solution is derived for the internal thermoelastic field describing stresses, strains, and displacements within the elliptical inhomogeneity.

Automated summary

In this study, we utilize the extended Stroh sextic formalism to solve the problem of an anisotropic elastic elliptical inhomogeneity embedded in an infinite anisotropic elastic matrix subjected to uniform remote heat flux. We rigorously prove that the remote thermal stresses cannot be eliminated in a generally anisotropic elastic matrix. Additionally, we derive a real-form solution describing the internal thermoelastic field within the elliptical inhomogeneity, including stresses, strains, and displacements.