On the spatial description in elasticity and the Doyle-Ericksen formula
type: Item
instance of: scholarly article
title: On the spatial description in elasticity and the Doyle-Ericksen formula
zbMATH Open document ID: 0803.73018
DOI: 10.1016/0045-7825(93)90178-Z
author: Carlo Sansour
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1994-01-02T00:00:00Z
review text: In some old papers (in Italian) Signorini mentioned already the advantages of using, in hyperelasticity, the `inverse' displacement and its `local' gradient. As the author notes here, `the use of certain stress or strain tensor(s) can be suitable (or not) in the sense that the formulation of the physical processes in terms of these tensors takes (or does not take) the (simplest) \(\ldots\) form'. In the paper the free energy is taken to be a function of the Almansi strain tensor, leading to relations well suited for a spatial description. The consequent corollaries, here precisely detailed, may be relevant beyond elasticity theory.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74A99
zbMATH DE Number: 473272
zbMATH Keywords: hyperelasticity
zbMATH Keywords: free energy
zbMATH Keywords: Almansi strain tensor
reviewed by: Gianfranco Capriz
MaRDI profile type: Publication
cites work: Q3335096
cites work: On the rotated stress tensor and the material version of the Doyle- Ericksen formula
cites work: The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates
cites work: A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. I: Continuum formulation
cites work: Q4023641
cites work: Q4066685
cites work: Manifolds, tensor analysis, and applications.
cites work: Semidirect Products and Reduction in Mechanics
cites work: Aspects of Invariance in Solid Mechanics
cites work: Q4201404
cites work: A study on rate-type constitutive equations and the existence of a free energy function
full work available at URL: 0045-7825(93)90178-z
OpenAlex ID: W2061906051
description: scientific article; zbMATH DE number 473272