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A unified evolution equation for the Cauchy stress tensor of an isotropic elasto-visco-plastic material. I. On thermodynamically consistent evolution

Fang, Chung and Wang, Yongqi and Hutter, Kolumban :
A unified evolution equation for the Cauchy stress tensor of an isotropic elasto-visco-plastic material. I. On thermodynamically consistent evolution.
[Online-Edition: http://www.springerlink.com/content/k50635j42m3w4016/]
In: Continuum Mechanics and Thermodynamics, 19 (7) pp. 423-440. ISSN 0935-1175
[Article] , (2008)

Official URL: http://www.springerlink.com/content/k50635j42m3w4016/

Abstract

In the present study an evolution equation for the Cauchy stress tensor is proposed for an isotropic elasto-visco-plastic continuum. The proposed stress model takes effects of elasticity, viscosity and plasticity of the material simultaneously into account. It is ascribed with some scalar coefficient functions and, in particular, with an unspecified tensor-valued function N, which is handled as an independent constitutive quantity. It is demonstrated that by varying the values and the specific functional forms of these coefficients and N, different known models in non-Newtonian rheology can be reproduced. A thermodynamic analysis, based on the Müller-Liu entropy principle, is performed. The results show that these coefficients and N are not allowed to vary arbitrarily, but should satisfy certain restrictions. Simple postulates are made to further simplify the deduced general results of the thermodynamic analysis. They yield justification and thermodynamic consistency of the existing models for a class of materials embracing thermoelasticity, hypoelasticity and in particular hypoplasticity, of which the thermodynamic foundation is established successively for the first time in literature. The study points at the wide applicability and practical usefulness of the present model in different fields from non-Newtonian fluid to solid mechanics. In this paper the thermodynamic analysis of the proposed evolution-type stress model is discussed, its applications are reported later.

Item Type: Article
Erschienen: 2008
Creators: Fang, Chung and Wang, Yongqi and Hutter, Kolumban
Title: A unified evolution equation for the Cauchy stress tensor of an isotropic elasto-visco-plastic material. I. On thermodynamically consistent evolution
Language: English
Abstract:

In the present study an evolution equation for the Cauchy stress tensor is proposed for an isotropic elasto-visco-plastic continuum. The proposed stress model takes effects of elasticity, viscosity and plasticity of the material simultaneously into account. It is ascribed with some scalar coefficient functions and, in particular, with an unspecified tensor-valued function N, which is handled as an independent constitutive quantity. It is demonstrated that by varying the values and the specific functional forms of these coefficients and N, different known models in non-Newtonian rheology can be reproduced. A thermodynamic analysis, based on the Müller-Liu entropy principle, is performed. The results show that these coefficients and N are not allowed to vary arbitrarily, but should satisfy certain restrictions. Simple postulates are made to further simplify the deduced general results of the thermodynamic analysis. They yield justification and thermodynamic consistency of the existing models for a class of materials embracing thermoelasticity, hypoelasticity and in particular hypoplasticity, of which the thermodynamic foundation is established successively for the first time in literature. The study points at the wide applicability and practical usefulness of the present model in different fields from non-Newtonian fluid to solid mechanics. In this paper the thermodynamic analysis of the proposed evolution-type stress model is discussed, its applications are reported later.

Journal or Publication Title: Continuum Mechanics and Thermodynamics
Volume: 19
Number: 7
Publisher: Springer
Uncontrolled Keywords: Stress tensor; Hypoelasticity; Hypoplasticity; Müller–Liu entropy principle
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 24 Aug 2011 18:11
Official URL: http://www.springerlink.com/content/k50635j42m3w4016/
Additional Information:

doi:10.1007/s00161-007-00

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