Elasticity of Gaussian and nearly-Gaussian phantom networks

Abstract

We study the elastic properties of phantom networks of Gaussian and nearly-Gaussian springs. We show that the stress tensor of a Gaussian network coincides with the conductivity tensor of an equivalent resistor network, while its elastic constants vanish. We use a perturbation theory to analyze the elastic behavior of networks of slightly non-Gaussian springs. We show that the elastic constants of phantom percolation networks of nearly-Gaussian springs have a power low dependence on the distance of the system from the percolation threshold, and derive bounds on the exponents.

submitted to Phys. Rev. E, 10 pages, 1 figure

References in corpus (1)

• Conductivity Exponent and Backbone Dimension in 2-d Percolation

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