A thermodynamic approach to rate-type models of elastic-plastic materials
type: Item
instance of: scholarly article
title: A thermodynamic approach to rate-type models of elastic-plastic materials
zbMATH Open document ID: 1489.74002
published in: Journal of Elasticity
publication date: 2022-01-25T00:00:00Z
review text: The objective of the paper is to derive rate-independent models, which are either non-dissipative, or dissipative and compatible with the second law of thermodynamics. Under the supposition that the Helmholtz (or Gibbs) free energy and the product of entropy, called the rate of dissipation (denoted by \(\Gamma\), with \(\Gamma \geq 0\)), are constitutive functions dependent on a certain set of independent variables, the second law of thermodynamics is reduced to the appropriate dissipation equalities in Section 3 and 4. The dissipation equalities (9) and (14) are written in terms of symmetric Piola-Kirchhoff, \(T_{RR}\), Green-St. Venant deformation tensor, \(E\), and their time derivative, with respect to the reference configuration. By passing to the Eulerian description, the dissipation equalities are rewritten under the form (10) and (15) in terms of Cauchy stress, Eulerian Almansi strain tensor, and their objective derivatives, namely Truesdell stress derivative and stretching tensor, respectively. In Section 5 the three-dimensional, finite deformation models are derived for special selections of \(\Gamma\), namely \(\Gamma\) depends either on \(\displaystyle{\frac{d}{d t}} E,\) \(\displaystyle{\frac{d}{d t}} T_{RR},\) via their norms, or on stress power \(T_{RR} \cdot \displaystyle{\frac{d}{d t}} E,\) with appropriate rate-independent non-negative, proportional factors. When these factors are vanishing, the non-dissipative models follow. Based on the decomposition of a second-order tensor given in Proposition 1, the Truesdell hypo-elastic type, rate-independent, but non-dissipative models are provided in the reference configuration, (20), while their counterpart, (24), written in the spatial description, expresses the Truesdell stress derivative as linear tensor function with respect to the stretching tensor. The rate-independent constitutive equations (23) and (25) are associated with general dissipative equations using the same decomposition result. The ment…
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74C15
Mathematics Subject Classification ID: 74A15
zbMATH DE Number: 7464177
zbMATH Keywords: large-strain rate-independent material
zbMATH Keywords: hypoelastic-plastic constitutive relation
zbMATH Keywords: one-dimensional model
zbMATH Keywords: free energy
zbMATH Keywords: entropy production
zbMATH Keywords: dissipation rate
author: Claudio Giorgi
author: Angelo Morro
reviewed by: Sanda Cleja-Ţigoiu
MaRDI profile type: Publication
full work available at URL: s10659-021-09871-3
OpenAlex ID: W4200464696
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DOI: 10.1007/S10659-021-09871-3
description: scientific article; zbMATH DE number 7464177