Variational bounds of elastic constants in transversely isotropic plates

Summary

The spectral decomposition of the fourth-rank compliance tensor S for transversely isotropic plates yields three eigenvalues, together with a new dimensionless parameter ω _p , called the plane eigenangle. These constitute the essential parameters for an invariant description of the elastic behaviour of anisotropic plates. In this paper, a study of the variational bounds imposed by thermodynamical constraints on the values of the elastic constants is presented. Furthermore, a theoretical definition of the longitudinal shear modulus G _L is introduced in terms of the elastic constants E _L , E _T and v _L as a means of checking the validity of the experimentally measured value of G _L . Finally, it is shown that the plane eigenangle ω _p is the only necessary parameter required for a monoparametric indication of the elasticity and toughness of transversely isotropic plates.