Journal ArticleDOI
On the Formulation of Rheological Equations of State
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The invariant forms of rheological equations of state for a homogeneous continuum, suitable for application to all conditions of motion and stress, are discussed in this article, where the right invariance properties can most readily be recognized if the frame of reference is a co-ordinate system convected with the material.Abstract:
The invariant forms of rheological equations of state for a homogeneous continuum, suitable for application to all conditions of motion and stress, are discussed. The right invariance properties can most readily be recognized if the frame of reference is a co-ordinate system convected with the material, but it is necessary to transform to a fixed frame of reference in order to solve the equations of state simultaneously with the equations of continuity and of motion. An illustration is given of the process of formulating equations of state suitable for universal application, based on non-invariant equations obtained from a simple experiment or structural theory. Anisotropic materials, and materials whose properties depend on previous rheological history, are included within the scope of the paper.read more
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Microfluidics: Fluid physics at the nanoliter scale
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The hydrodynamics of swimming microorganisms
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Book ChapterDOI
Stress-Deformation Relations for Isotropic Materials
Ronald S. Rivlin,J. L. Ericksen +1 more
TL;DR: In this article, it was shown that the mechanics of a homogeneous isotropic ideally elastic material may be developed on the basis of a description of the relevant elastic properties of the material in terms of a strain energy function W which is a single-valued function of three scalar invariants of the deformation, I 1, I 2 and I 3.
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Journal ArticleDOI
A continuum theory of rhelogical phenomena
TL;DR: In this article, the authors focus on a group of rheological phenomena which allow a theoretical and experimental investigation on a macroscopic scale, and treat the materials as continuous media, and the forces and displacements as vectors which vary continuously in space and time.