Complex Form of Hooke's Law of Anisotropic Elastic Body.

A complex form of Hooke's law for an anisotropic body is given, which made it possible to write down the previously known relations obtained in the simplest way. The structure of the matrix of elastic parameters and six linear invariants, which play a key role both in the connection of the stress-strain state and in the structure of the matrix of elastic parameters, have been determined. It is shown that by a certain six-dimensional unitary transformation, constructed on the basis of Hausholder matrices, the matrix of elastic moduli is reduced to the canonical form, in which the elastic moduli are invariants. Some questions of the classification of elastic materials are discussed. Formulas for the transformation of elastic moduli under three-dimensional rotation are given, as well as examples of anisotropic materials with certain properties. The possibility of constructing six invariant forms of Hooke's law is shown. [ABSTRACT FROM AUTHOR]