Affine transforms of three-dimensional anisotropic media and explicit formulas for fundamental matrices

The concept of classes of algebraically equivalent anisotropic three-dimensional media is introduced: elastic fields in such media are related by simple algebraic expressions. An explicit formula is obtained for a fundamental matrix with ten free constants in the elastic modulus tensor (rather than for five free constants, as in the famous case of transverse isotropy). A hypothesis is formulated and several questions are posed, which are related to the notion of algebraic equivalence under discussion.