On the spatial description in elasticity and the Doyle-Ericksen formula
In some old papers (in Italian) Signorini mentioned already the advantages of using, in hyperelasticity, the `inverse' displacement and its `local' gradient. As the author notes here, `the use of certain stress or strain tensor(s) can be suitable (or not) in the sense that the formulation of the physical processes in terms of these tensors takes (or does not take) the (simplest) \(\ldots\) form'. In the paper the free energy is taken to be a function of the Almansi strain tensor, leading to relations well suited for a spatial description. The consequent corollaries, here precisely detailed, may be relevant beyond elasticity theory.
scientific article; zbMATH DE number 473272
scientific article