Inner elasticity

Abstract

For crystals in which inner displacement is possible there exists a group of tensors whose members (called inner elastic constants) are derivatives of the energy with respect to at least one component of inner displacement. A consistent, simple tensorial notation is introduced for the six types that arise when the energy of deformation is expanded to third order in the strain. Each inner elastic constant is shown to be composed of a sum of more fundamental interlattice tensors. An account is given of the basic definitions of inner displacement, of the expansion of the energy in terms of partial and inner elastic constants, of extra equilibrium conditions, of the decomposition of the total elastic constants into parts dependent on different orders of internal strain and, finally, of the relationship between this formalism and that of lattice dynamics in the limit of zero wavevector.