On the formulation of rheological equations of state

1950/02/22 by J. G. Oldroyd · 2,028 citations
Chemical Engineering · Engineering · Mathematics · #Anisotropy #Classical mechanics #Computer science #Differential equation #Elasticity and Material Modeling #Elasticity and Wave Propagation #Equations of motion #Frame (networking) #Homogeneous #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Reference frame #Rheology #Rheology and Fluid Dynamics Studies #Simultaneous equations #Thermodynamics

paper · doi:10.1098/rspa.1950.0035

published in Proceedings of the Royal Society of London A Mathematical and Physical Sciences 200(1063), 523-541 (Royal Society)

openalex publication_date 1950/02/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/25

Abstract

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.

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