On Hooke's law
A novel method of describing elastic anisotropy based on the concept of an elastic eigen-state is proposed. The structure of the rigidity tensor is determined. In particular, it is shown that the set of 21 constants describing continuously the manifold of elastic solids is composed of three different subsystems: 6 true rigidity moduli, 12 dimensionless rigidity distributors, and 3 invariant parameters defining the orientation of the body in question relative to the laboratory system of coordinates. It is shown that Hooke's law can be written uniquely for an arbitrary anisotropic body in the form of several laws describing the direct proportionality of the corresponding parts of the stress and deformation tensors. The construction of these parts is illustrated using an example of a transversally isotropic solid.
scientific article; zbMATH DE number 3930428
scientific article