Expressions for Objective Co-Rotational Rates of Eulerian Stress Tensors

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Alan, Mehdi | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41844 (08)
University: Sharif University of Technology
Department: Mechanical Engineering
Advisor(s): Asghari, Mohsen
Abstract:
Stress tensors and their rates are fundamental quantities in modeling the behavior of materials in the field of nonlinear continuum mechanics. One of the most remarkable applications of stress rates is their presence in the rate type constitutive equations of materials.
Co-rotational rates are corresponding to the rates which are measured by an observer who is in a reference rotating coordinate system. In general, under some specific conditions for the spin of a co-rotational rate, the rate of an Eulerian tensor would be objective. In this thesis, the objective co-rotational rates of Eulerian stress tensors for isotropic elastic materials under large deformations are obtained for the most general form of the objective co-rotational rates. At first, the component form of the objective co-rotational rates is obtained under all cases of distinct and coalescent principal stretches. Then, the invariant objective co-rotational rates of Eulerian stress tensors are presented under all cases of distinct and coalescent principal stretches in terms of left stretch tensor, V and strain rate tensor, D
Keywords:
OBJECTIVE RATES ; Corotational Rates ; Nonlinear Continuum Mechanics ; Eulerian Stress ; Linear Elastic Isotropic Materials ; Invariant Form