Many kinds of high polymer substances show the viscoelsstic behavior in their amorphous solid states, melting states, concentrated solutions, etc. As a model of these properties, we consider the subber-like network in which. But, the polymer chains constracting it are broken and reformed with time, and under the assumption that the deformation of material is so late that the statistical mechanical considerations can be applied in this system for each “instance” of macroscopic observations, we culculate the strain-stress-time relation. These ideas are essentially equivalent to those in Green-Tobolsky's paper. 3. In order to obtain these relations, we consider the distribution function of the chains forming the network and the differential equation satisfied by it with respect to the time (it corresponds to Maxwell-Boltymann equation in the case of gases), while in Green-Tobolsky's paper, they started form the integral equation between strain and stress with respect to the time. Moreover, our calculation is more general in the process of breaking and reformation of chain than their one. our result is as follows:
dσ/dt=dα/dtα
-1σ+σα
+-1dα
+/dt-P[dα/dtα
-1+α
+-1dα
+/dt]+dP/dt1+(dσ/dt)
b, r.
where σ is the stress tensor. α the strain tensor, α
+ the transposed tensor of α, P a scalar quantity corresponding the pressure, 1 the unit tensor, and, (dσ/dt)
b, r the variation of stress due to breaking and reformation of chains.
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