Stress-Strain Behavior of Crosslinked Elastomers

Consider a cube of crosslinked elastomer subjected to a tensile force /. The ratio of the increase in length to the unstretched length is the nominal strain, e, 

For a cube of unit initial dimensions, di = iodX = dX and the stress cr is equal to the force /. Equation (2.70) is thus equivalent to 

From statistical mechanical calculations (Treloar, 1975) it can be shown that the entropy of deformation is given by 

For an ideal network the quantity pNAy In (where p is the elastomer density, gram per unit volume) is defined as. the average molecular weight of chain lengths between crosslinks, denoted by Me- So, 

Me is a basic variable characterizing the network structure. A high value of Me implies a more tightly crosslinked structure. Hence 1/Mc may be taken as a measure of the degree of crosslinking. 

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