The inverse problem of coupled thermoelasticity is considered in the static, quasi-static, and dynamic cases. The goal is to recover the thermal stress state inside a body from the displacements and temperature given on a portion of its boundary. The inverse thermoelasticity problem finds applications in structural stability analysis in operational modes, when measurements can generally be conducted only on a surface portion. For a simply connected body consisting of a mechanically and thermally isotropic linear elastic material, uniqueness theorems are proved in all the cases under study.
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