An algebra of tensor operators and its applications to elasticity

Abstract An algebra of tensors of order four which depend on a unit vector and the Kronecker delta is investigated. It is shown that the algebra has natural applications in classical elasticity as well as in the continuum theory of dislocations. Explicit formulas for the corresponding Green's functions and projection operators are obtained. It is shown that a remarkable correspondence exists between global projection operators and local ones associated with strain and stress jumps at surfaces of discontinuity. This correspondence affords a unified treatment for global and local projection operators.