Coordinate-free characterization of the symmetry classes of elasticity tensors

DOI10.1007/s10659-007-9099-zzbMath1151.74309OpenAlexW1997808578MaRDI QIDQ2642638

Andrej Bóna, Ioan Bucataru, Michael A. Slawinski

Publication date: 17 August 2007

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10659-007-9099-z

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Classical linear elasticity (74B05)

Related Items (17)

Non-Gaussian positive-definite matrix-valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries ⋮ Generalized stochastic approach for constitutive equation in linear elasticity: a random matrix model ⋮ On the isotropic moduli of 2D strain-gradient elasticity ⋮ Two complementary methods of inferring elastic symmetry ⋮ On the algebraic structure of isotropic generalized elasticity theories ⋮ A stochastic model for elasticity tensors with uncertain material symmetries ⋮ On the Backus average of a layered medium with elasticity tensors in random orientations ⋮ Algebra of transversely isotropic sixth order tensors and solution to higher order inhomogeneity problems ⋮ Identifying symmetry classes of elasticity tensors using monoclinic distance function ⋮ Space of 2D elastic materials: a geometric journey ⋮ On anisotropic polynomial relations for the elasticity tensor ⋮ Generic separating sets for three-dimensional elasticity tensors ⋮ Invariant properties for finding distance in space of elasticity tensors ⋮ The number and types of all possible rotational symmetries for flexoelectric tensors ⋮ 2-norm effective isotropic Hookean solids ⋮ Characterization of the symmetry class of an elasticity tensor using polynomial covariants ⋮ Kelvin decomposition for nonlinear hyperelastic modeling in large deformation

Cites Work

• Unnamed Item
• Unnamed Item
• The structure of the linear anisotropic elastic symmetries
• On Hooke's law
• On the completeness of crystallographic symmetries in the description of the symmetries of the elastic tensor
• On the polynomial invariants of the elasticity tensor
• Symmetry classes for elasticity tensors
• Symmetry classes and harmonic decomposition for photoelasticity tensors
• Generalized Cowin-Mehrabadi theorems and a direct proof that the number of linear elastic symmetries is eight
• The anisotropic Hooke's law for cancellous bone and wood
• ON THE IDENTIFICATION OF MATERIAL SYMMETRY FOR ANISOTROPIC ELASTIC MATERIALS
• Optimal orientation of anisotropic solids
• EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS
• Fourth-rank tensors of the thirty-two crystal classes: multiplication tables
• Classification of symmetry by means of Maxwell multipoles
• Material symmetries of elasticity tensors
• Spectral Decomposition of the Elasticity Tensor
• A new proof that the number of linear elastic symmetries is eight

This page was built for publication: Coordinate-free characterization of the symmetry classes of elasticity tensors