Elastic network central force

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)). 

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... 

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... 

Accurate numerical studies, using this self-consistent strain calculation method for various elastic networks, with central and bond-bending forces, by Sahimi and Arbabi (1993) gave Tf = 2.42 0.14 and = 2.64 0.3 in d = 2 and 3 respectively. These estimates again compare well with the experimental results of Benguigui et al (1987) ind = 2, and fall within the above-mentioned theoretical bounds (given by (3.14)). 

They considered both central force as well as the bond-bending models. In the latter (bond-bending model), the elastic energy (H) of the network is contributed both by the central force (spring constant) part and the... 

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