On anisotropic polynomial relations for the elasticity tensor

DOI10.1007/s10659-013-9448-zzbMath1410.74004OpenAlexW1966687966MaRDI QIDQ464304

J. Herrera, D. Rodríguez-Gómez

Publication date: 17 October 2014

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

Full work available at URL: https://doi.org/10.1007/s10659-013-9448-z

zbMATH Keywords

invariantbifurcation diagramBetten polynomialsisotropy classsymmetry class

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Classical linear elasticity (74B05) Anisotropy in solid mechanics (74E10)

Related Items

Extreme conditions of elastic constants and principal axes of anisotropy ⋮ Quadratic invariants of the elasticity tensor ⋮ Harmonic factorization and reconstruction of the elasticity tensor ⋮ Isotropic invariants of a completely symmetric third-order tensor ⋮ Handbook of bi-dimensional tensors: Part I: Harmonic decomposition and symmetry classes ⋮ A minimal integrity basis for the elasticity tensor ⋮ Distance to a constitutive tensor isotropy stratum by the Lasserre polynomial optimization method ⋮ A 6-ring embedded strain sensor ⋮ About Gordan's algorithm for binary forms ⋮ Computation of minimal covariants bases for 2D coupled constitutive laws ⋮ An Inverse Method to Get Further Analytical Solutions for a Class of Metamaterials Aimed to Validate Numerical Integrations ⋮ Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model ⋮ Space of 2D elastic materials: a geometric journey ⋮ Recovering the normal form and symmetry class of an elasticity tensor ⋮ Irreducible matrix resolution for symmetry classes of elasticity tensors ⋮ Minimal functional bases for elasticity tensor symmetry classes ⋮ Symmetry classes in piezoelectricity from second-order symmetries ⋮ Characterization of the symmetry class of an elasticity tensor using polynomial covariants ⋮ Green-Naghdi rate of the Kirchhoff stress and deformation rate: the elasticity tensor

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symmetry classes for even-order tensors
• Analytical expressions for anisotropic tensor dimension
• The geometry of spontaneous symmetry breaking
• Characterization of elasticity-tensor symmetries using \(SU(2)\)
• Proof of Hermann's theorem using the Forte-Vianello's method
• Inequalities defining orbit spaces
• On Hooke's law
• Lifting smooth homotopies of orbit spaces
• Singularities and groups in bifurcation theory. Volume II
• Determination of the symmetries of an experimentally determined stiffness tensor: Application to acoustic measurements
• On the polynomial invariants of the elasticity tensor
• Symmetry classes for elasticity tensors
• Coordinate-free characterization of the symmetry classes of elasticity tensors
• ON THE ACOUSTIC DETERMINATION OF THE ELASTIC MODULI OF ANISOTROPIC SOLIDS AND ACOUSTIC CONDITIONS FOR THE EXISTENCE OF SYMMETRY PLANES
• EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS
• Irreducible invariants of fourth-order tensors
• HARMONIC DECOMPOSITION OF THE ANISOTROPIC ELASTICITY TENSOR
• Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata
• PROPERTIES OF THE ANISOTROPIC ELASTICITY TENSOR
• On the Graded Ring of Invariants of Binary Octavics