Coupling between mechanical and thermodynamic processes can be significant in solid media when material inelasticity occurs. Significant mechanical energy may be converted into heat via hysteretic loss, and this coupling may be significant even under quasi-static conditions. Important advances have been made since the second world war in modeling this thermomechanical coupling. This paper reviews many of the major achievements on this subject. The paper opens with a short review of historical milestones on the subject. A theoretical model is then reviewed, including both conservation laws and constitutive models for certain classes of solids. The paper concludes with a discussion of recent attempts to solve the inelastic coupled thermomechanical field problem.

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