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Non-Conventional Thermodynamics and Models of Gradient Elasticity

Alber, Hans-Dieter and Broese, Carsten and Tsakmakis, Charalampos and Beskos, Dimitri (2018):
Non-Conventional Thermodynamics and Models of Gradient Elasticity.
In: Entropy, MDPI, 20, (3), ISSN 1099-4300,
DOI: 10.3390/e20030179,
[Online-Edition: https://doi.org/10.3390/e20030179],
[Article]

Abstract

We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toupin–Mindlin’s type, i.e., a theory employing Cauchy stress tensors, which are not necessarily expressed as Euler–Lagrange derivatives. This is accomplished in the framework of non-conventional thermodynamics. A one-dimensional boundary value problem is solved in detail in order to illustrate the differences of the present theory with Toupin–Mindlin’s gradient elasticity theory.

Item Type: Article
Erschienen: 2018
Creators: Alber, Hans-Dieter and Broese, Carsten and Tsakmakis, Charalampos and Beskos, Dimitri
Title: Non-Conventional Thermodynamics and Models of Gradient Elasticity
Language: English
Abstract:

We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toupin–Mindlin’s type, i.e., a theory employing Cauchy stress tensors, which are not necessarily expressed as Euler–Lagrange derivatives. This is accomplished in the framework of non-conventional thermodynamics. A one-dimensional boundary value problem is solved in detail in order to illustrate the differences of the present theory with Toupin–Mindlin’s gradient elasticity theory.

Journal or Publication Title: Entropy
Volume: 20
Number: 3
Publisher: MDPI
Divisions: 13 Department of Civil and Environmental Engineering Sciences > Mechanics > Continuum Mechanics
13 Department of Civil and Environmental Engineering Sciences > Mechanics
13 Department of Civil and Environmental Engineering Sciences
Date Deposited: 18 Mar 2018 20:55
DOI: 10.3390/e20030179
Official URL: https://doi.org/10.3390/e20030179
URN: urn:nbn:de:tuda-tuprints-72954
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