A qualitative approach to Hooke's tensors. Part I

Abstract

The main qualitative properties of Hooke's tensors can be found in their invariant decompositions, both linear and nonlinear. The invariant nonlinear spectral decompositions are presented in the review [7] and the papers quoted therein. This paper deals with linear invariant decompositions initiated in [12-20]. A straightforward and complete description of all such possible decompositions is presented here in Part I. The main results are given in formulae (7.1), (7.3). The next part (to appear), Part II, will contain derivations, conclusions and unexpected applications.