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. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 95–102, March–April, 2006.