Strain-energy function functions

Kawabata, S. and Kawai, H. Strain Energy Density Functions of Rubber Vulcanizates from Biaxial Extension. Vol. 24, pp. 89 — 124. 

Fig. 12 The meridianal orientation function p(0) for a Gaussian distribution, the distribution function p(0)sin0,the shear strain energy function tan20sin0p(0) and the function tan20...

Strain Energy Density Functions of Rubber Vulca-... 

II. The Strain Energy Density Function and the Phenomenolojpc Equation... 

III. Search for the Strain Energy Density Function of Vulcanized Rubbers. 95... 

In the present article, we summarize typical approaches to the evaluation of the strain energy density function from biaxial extension experiments and illustrate some intportant data. This article is not a review in the ordinary sense, as it deals to a large extent with a series of experiments carried out in our laboratory. By this we do not mean to bias or ignore any of the many important contributions by other authors. 

Our own experience, as well as that of other authors, has shown that very precise measurement for the stress-strain relationship under general biaxial deformation is required to investigate the behavior of the strain energy density function of rubber vulcanizates. Unfortunately, available biaxial extension data are still too meager to deduce the general form of the strain energy density function of rubber-like substances. We wish to take this opportunity to summarize the principal results from our recent efforts, in the hope that they may serve to illustrate the interesting and complex nature of the derivatives 31V/9/,- of such substances. 

From the viewpoint of the mechanics of continua, the stress-strain relationship of a perfectly elastic material is fully described in terms of the strain energy density function W. In fact, this relationship is expressed as a linear combination erf the partial derivatives of W with respect to the three invariants of deformation tensor, /j, /2, and /3. It is the fundamental task for a phenomenologic study of elastic material to determine W as a function of these three independent variables either from molecular theory or by experiment. The present paper has reviewed approaches to this task from biaxial extension experiment and the related data. The results obtained so far demonstrate that the kinetic theory of polymer network does not describe actual behavior of rubber vulcanizates. In particular, contrary to the kinetic theory, the observed derivative bW/bI2 does not vanish. 

Valanis,K.C., Landel,R.F. The strain-energy function of a hyperelastic material in terms of extension ratios. J. Appl. Phys. 38,2997-3002 (1967). 

The analysis of Eq. (16) has led to the conclusion 7) that the strain-energy function W in the mode of uniform deformation is parabolic with a minimum potential energy in the unstrained state... 

Figure 19.7 Elastic strain energy function E c/a) for an incoherent ellipsoid inclusion of aspect ratio c/a.

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