# On the formulation of rheological equations of state

@article{Oldroyd1950OnTF, title={On the formulation of rheological equations of state}, author={J. G. Oldroyd}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, year={1950}, volume={200}, pages={523 - 541} }

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… Expand

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#### References

SHOWING 1-4 OF 4 REFERENCES

A Continuum Theory of Rhelogical Phenomena

- Materials Science
- Nature
- 1947

WHEN materials of different kinds are subjected to mechanical actions we may observe a great variety of rheological phenomena, and we shall confine our attention here to a certain group of them which… Expand