Stress-Deformation Relations for Isotropic Materials

It has been shown (see C. Truesdell (1952) for a comprehensive review of this subject) 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.

[1]  E. Kamke,et al.  Differentialgleichungen reeller funktionen , 1931 .

[2]  M. Reiner,et al.  A Mathematical Theory of Dilatancy , 1945 .

[3]  M. Reiner.  Elasticity Beyond the Elastic Limit , 1948 .

[4]  R. Rivlin.  Large elastic deformations of isotropic materials IV. further developments of the general theory , 1948, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  R. Rivlin,et al.  The hydrodynamics of non-Newtonian fluids. I , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[6]  R. S. Rivlin,et al.  Large elastic deformations of isotropic materials. V. The problem of flexure , 1949, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  R. S. Rivlin,et al.  Large elastic deformations of isotropic materials VI. Further results in the theory of torsion, shear and flexure , 1949, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[8]  J. Oldroyd.  On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.