Remarks on the Eshelbian thermomechanics of materials

The notion of Legendre–Fenchel transformation is used jointly with that of continuum mechanics on the material manifold (so-called Eshelbian mechanics) in order to specify more easily the relevant thermodynamical regime. This has direct consequences in the formulation of the appropriate driving force acting on various singular surfaces. Thanks to the notion of material “thermal” force, the formalism also provides directly a proof of theorems such as those of Vazsonyi–Crocco, Helmholtz, and Bernoulli.