SOME PROPERTIES OF THE SET OF 4TH-ORDER TENSORS, WITH APPLICATION TO ELASTICITY

In this paper the algebraic structure of the set of fourth-order tensors is examined. Special emphasis is given to the two different tensor products which can be defined over this set, when it is regarded as a vector space and as the set of all linear transformations over a vector space, respectively. The new formalism introduced here makes it possible to write in a simple form the restrictions imposed on the elasticity tensors, in finite elasticity, by balance of angular momentum and by the principle of material frame-indifference. A reassessment of the various elasticity tensors used in the literature is presented, and some classical results are re-stated in a simple and natural way. © 1979 Sijthoff & Noordhoff International Publishers.