A Three Dimensional Treatment of the Viscoelasticity in Rubber-Like Substances

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The theoretical treatment of viscoelastic phenomena, such as appear in the stress-strain curves, in rubber-like, substances has been made abready by T. Sakai and others, concerning chiefly to one dimensional model of the network structure.In this paper, we have developed three dimensional treatment of the above-mentioned phenomena, basing on Sakais idea.In this case, we assume that (i) the joint point of the network are not permanent. i. e. the relative displacement between chains may take place, nevertheless rubber elasticity can be realized. (ii) the numder of segments constituting one chain is kept constant during any deformation.First we have gotten the equations giving the relations between the tione derivatives of the coordinates (x, y, z) of one end of the chain to the other end and the time derivativea of the macroscopic elongation ratio (r1, r2, r3) of the sample, and next have gotten the formulas representing the principal stresses which are given as the function of x, y, z, ; r1, r2, r3, Finally, we have applied the above equations to the problem of the uniform stretching in one direction, and carried the calculations for the cases of (i) dr/dt=0. (ii) dσ/dt=0, and (iii) dr/dt=const. The resuets not only agree with the results gained by one dimensional model qualitatively, but seems to give more details of the viscoelastic properties.
物性研究刊行会の論文