On the structure of the theory of polar elasticity

This work presents a study of the formal structure of the theory of finite–strain polar elasticity and thermoelasticity with special attention to the construction of canonical balance laws that concern the whole system under study and not only each separate degree of freedom. These are the balance of energy and so–called pseudo–momentum whose (i) local form plays an essential role in the theory of smooth material inhomogeneities (so–called gradient materials), (ii) global form, integrated over a material region, finds a direct application in the corresponding theory of fracture (expression of the energy–release rate and path–independent integrals) and (iii) associated jump equations provide a fruitful application in the theory of the progress of coherent phase–transition fronts obeying the second law of thermodynamics by relating the localized surface entropy and hot heat source to the kinetics of the front and helping one devise a criterion of progress. All corresponding expressions are obtained either in quasi–statics or in full dynamics. The untouched problems are those of completeness of the set of conservations laws, the much expected ‘geometrization’ of the theory, and the generalization to incoherent phase–transition fronts for which dislocations and disclinations will play a foremost role. Hints for the solution of these three problems are given.