A note on stress/strain conjugate pairs: Explicit and implicit theories of thermoelasticity for anisotropic materials

A set of six, independent, stress/strain, conjugate pairs are derived: One for dilation, two for squeeze, and three for shear. They follow from a Gram-Schmidt factorization of the deformation gradient. Theories for elastic solids are derived in terms of these conjugate pairs. Anisotropy is introduced through bijective maps between tensor components and constituents of the basis. The boundary value problems of simple tension and uniform pressure are used to illustrate the effects of anisotropy, as predicted by a Hooke-like material model.