Nonlinear elasticity of prestressed single crystals at high pressure and various elastic moduli

A general nonlinear theory for the elasticity of prestressed single crystals is presented. Various types elastic moduli are defined, their importance determined, and relationships between them In particular, $\mathbit{B}$ present in relationship Jaumann objective time derivative Cauchy stress deformation rate broadly used computational algorithms various finite-element codes. Possible applications to simplified linear solutions complex problems outlined illustrated a superdislocation. The effect finite rotations fully taken into account analyzed. Different bulk shear under different constraints defined connected effective properties polycrystalline aggregates. Expressions energy stress-strain small distortions with respect configuration derived detail. Under initial hydrostatic load, consistency conditions compliances that follow from existence generalized tensorial equation state loading obtained crystal or polycrystal. It shown can be found expression Gibbs energy. However, higher order do not have any meaning since they directly participate known equations, like wave propagation equation. deviatoric projection also isochoric strain increments, missing components conditions.