Random spring network

Central force elastic percolation If one considers an elastic network of springs, which can provide only the central force, and not the bond-bending force considered earlier, then the elastic energy of such a random bond network can be expressed by the same energy function H in (1.11) with... 

Similarly, one can study the growth of the elastic constants (say the rigidity modulus) of a randomly formed elastic network, near the percolation point. The central force elastic problem (for networks formed out of linear springs only) belongs however to a different class of percolation problem, known as elastic percolation or central force percolation, and is discussed separately later (see Section 1.2.1(f)). 

The growth of the elastic modulus Y of such a random central force network with p > pce again follows a power law Y (P - Pce) "- The available estimates for Tce/i ce — 1.12 0.05 in d = 2. Also, for superelastic percolation with central force, where a fraction p of the bonds (springs) are infinitely rigid and the rest are central force springs (with finite spring... 

Sahimi and Arbabi (1993) considered the fracture properties of an elastic network where each bond has a fixed spring constant (k) but the critical or threshold strain or the bond-length Oc is randomly distributed following the distribution... 

When a polymer network goes inside an FLC medium, we may consider the random networks of cross-Unk chains to be stretched between two smectic planes spaced L apart (Fig. 6.5). Gaussian like cross-links with orientationally uncorrelated chains, freely joined by spherical particles and connected by harmonic springs can be considered as shown in Fig. 6.6. r(z) = [x(z),y(z)], describes the path of cross links conformations where z stands for the direction of cross-link alignment without any loops and overhangs. Further, we assume the cross-link... 

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