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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. (English) Zbl 1170.74309
Summary: 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.

MSC:
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74A15 Thermodynamics in solid mechanics
74B20 Nonlinear elasticity
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