The Meaning of Betti's Reciprocal Theorem

It was remarked long ago (1)1 that Betti 's l'eciprocal theorem, famili ar in the linearized theory of elasticity, remains valid for infinitesi mal strain superimposed upon fLn arbitmrily strained tate of a hyperelastic material, and recently a proof was published [2]. The true significance of Betti's theorem, however, lies in its being a criterion jor the existence oj a stored-energy junction. Indeed, the differen t ial equations and stress boundary conditions to be sl1tisfied by the superimposed displacement field u are [3]