Representations for transversely hemitropic and transversely isotropic stress-strain relations
Copyright policy )Representations for transversely hemitropic and transversely isotropic stress-strain relations
The author derives a representation for the set of constitutive equations for the second Piola-Kirchhoff stress tensor for a simple elastic material point when the material is either transversely hemitropic or transversely isotropic. The author restricts his attention to polynomial stress-strain relations. The sets of stress-strain relations are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established by using Cartan decomposition of the representation of the adjoint action of two-dimensional rotation and orthogonal groups on the space of 3 by 3 symmetric matrices. The results are compared to the representations known from the literature.
- United States Naval Academy United States
Cartan decomposition, polynomial stress-strain relations, Linear elasticity with initial stresses, Theory of constitutive functions in solid mechanics, Nonlinear elasticity, Anisotropy in solid mechanics, second Piola-Kirchhoff stress tensor, projections of free algebraic modules, rotation and orthogonal groups
Cartan decomposition, polynomial stress-strain relations, Linear elasticity with initial stresses, Theory of constitutive functions in solid mechanics, Nonlinear elasticity, Anisotropy in solid mechanics, second Piola-Kirchhoff stress tensor, projections of free algebraic modules, rotation and orthogonal groups
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