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A Theory of Large Elastic Deformation

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1 Author(s)
Mooney, M. ; United States Rubber Company, Passaic, New Jersey

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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=
 G 
 4 
3
i=1
λi-
 1 
 λi 
2+
 H 
 4 
3
t=1
λi2-
 1 
 λi2 
,
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 σi[minus]σii∂ W/∂λi[minus]λi∂ W/∂λi. Calculated forces agree closely with experimental data on soft rubber from 400 percent elongation to 50 percent compression.

Published in:

Journal of Applied Physics  (Volume:11 ,  Issue: 9 )