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It is postulated that (A) the material is isotropic, (B) the volume change and hysteresis are negligible, and (C) the shear is proportional to the traction in simple shear in a plane previously deformed, if at all, only by uniform dilatation or contraction. It is deduced that the general strain-energy function, W, has the form W=G4 ∑ i=13(λi−1λi)2+H4 ∑ t=13(λi2−1λi2),where the λi's are the principal stretches (1+principal extension), G is the modulus of rigidity, and H is a new elastic constant not found in previous theories. The differences between the principal stresses are σiminusσi=λi∂ W/∂λiminusλi∂ W/∂λi. Calculated forces agree closely with experimental data on soft rubber from 400 percent elongation to 50 percent compression.
M. Mooney (Sun,) studied this question.
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