Network Models with Some Non-Classical Character

Network Models with Some Non-Classical Character 

One could also construct a network involving elements which allow some adjustment in the location of their coupling points in response to deformation. Consider a tetrahedral network element (3) in which two gaussian strands of equal contour length are attached to the comers and joined together at their midpoints by a crosslink  

If the network is given a tensile deformation in the 2 direction and the comers move affinely, the four chains in the tetrahedron contribute independently to the modulus, with the well known result obtained from the rubber elasticity theory  

If the crosslink is removed, the system reverts to two independent chains. To preserve the symmetry of the system one needs to consider the average for three tetrahedra operating together, one for each of the three possible pairings of the strands. The result is again neo-Hookean behavior but with a lower modulus contribution. 

An intermediate situation is obtained if the central crosslink is replaced by a slipping link such that the two chains are constrained to be in contact at one 

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