What question did this study set out to answer?

To establish mathematically invariant forms of rheological equations of state for homogeneous continuous media under arbitrary conditions of motion and stress.

February 22, 1950Proceedings of the Royal Society of London A Mathematical and Physical Sciences

On the formulation of rheological equations of state

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Authors

JOJ. G. OldroydWest Virginia Wesleyan College

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Implication

Theoretical analysis demonstrates invariant rheological equations of state using convected coordinates, indicating universal applicability across complex materials and deformation histories.

Key Points

To establish mathematically invariant forms of rheological equations of state for homogeneous continuous media under arbitrary conditions of motion and stress.
Utilized a coordinate system convected with the deforming material to naturally define invariant constitutive relations.
Formulated mathematical transformations to convert convected-frame equations into fixed reference frames for simultaneous solution with equations of motion and continuity.
Generalized the formulation to account for directional dependencies (anisotropy) and memory effects from prior rheological deformation history.
Demonstrated that valid universal constitutive equations can be systematically constructed from simple one-dimensional experiments or structural theories.
Showed that transforming equations from material-bound frames to fixed spatial coordinates preserves frame-indifference while allowing boundary-value flow solutions.

Cite This Study

J. G. Oldroyd (1950) studied this question.

synapsesocial.com/papers/69d708e49f004159b8aa7e8b https://doi.org/10.1098/rspa.1950.0035

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Implication

Theoretical analysis demonstrates invariant rheological equations of state using convected coordinates, indicating universal applicability across complex materials and deformation histories.

On the formulation of rheological equations of state

Discussion

Member takes

Implication

Key Points

Cite This Study

On the formulation of rheological equations of state

Discussion

Member takes

Implication

Key Points

Cite This Study

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