An approach to isotropic tensor functions and their derivatives via omega matrix calculus

DOI10.1007/s10659-020-09775-8zbMath1447.74006OpenAlexW3031601985MaRDI QIDQ2202457

Antônio Francisco Neto

Publication date: 18 September 2020

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

Full work available at URL: https://doi.org/10.1007/s10659-020-09775-8

zbMATH Keywords

Cayley-Hamilton theorempartition analysismatrix analysishigher-order derivative

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99)

Related Items (1)

Unnamed Item

Uses Software

• Omega

Cites Work

• Unnamed Item
• Unnamed Item
• Some indentities for the gradient of the principal invariants, traces and determinants via Grassmann calculus
• Derivatives of the principal invariants of a second-order tensor
• On the derivative of the square root of a tensor and Guo's rate theorems
• On the derivatives of the principal invariants of a second-order tensor
• Some properties of the set of fourth-order tensors, with application to elasticity
• Derivatives of the stretch and rotation tensors
• On the gradients of the principal invariants of a second-order tensor
• Computation of the exponential and other isotropic tensor functions and their derivatives.
• Derivatives and rates of the stretch and rotation tensors
• On the derivation for the gradients of the principal invariants
• A note on Rivlin's identities and their extension
• Perturbation theory for linear operators.
• A closed-form representation for the derivative of non-symmetric tensor power series
• Derivatives of the stretch, rotation and exponential tensors in \(n\)-dimensional vector spaces
• Derivatives on the isotropic tensor functions
• Higher derivatives and the inverse derivative of a tensor-valued function of a tensor
• The derivative of a tensor-valued function of a tensor
• Improving the Cayley-Hamilton Equation for Low-Rank Transformations
• The Cayley-Hamilton Theorem
• Application of the Dunford-Taylor integral to isotropic tensor functions and their derivatives
• Derivative of a function of a nonsymmetric second-order tensor
• Matrix Analysis and Omega Calculus
• MacMahon's partition analysis: The Omega package

This page was built for publication: An approach to isotropic tensor functions and their derivatives via omega matrix calculus