The relation between invariant integrals of the linear isotropic theory of elasticity and integrals defined by the duality principle

Invariant integrals of the linear isotropic theory of elasticity, determined by a certain specified elastic field, are considered, and also invariant integrals generated by the interaction of the specified field with an arbitrary secondary field. For all types of invariant integral, generated by the interaction of the specified elastic field and an arbitrary secondary elastic field, transformations of the secondary fields are found for which the invariant integrals considered turn out to be equal to the RG-integrals, determined by the duality principle, of the specified elastic field and the transformed secondary elastic field. The invariant J-, L- and M-integrals themselves are also expressed in terms of the RG-integrals of the specified elastic field and its corresponding transformation.