Long-range correlations of elastic fields in semi-flexible fiber networks
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The mechanical properties of semi-flexible networks have been the subject of intense theoretical and experimental studies concerned primarily with the understanding of the complex behavior of biological systems such as the cell. Here it is shown that the elasticity of these networks, both elastic constants and elastic fields, while fluctuating significantly with position, is long-range correlated and the correlation functions exhibit power law scaling. The correlations are lost when the fiber stiffness is reduced. The range of scales over which correlations are observed is bounded below by the mean fiber segment length and above by the filament persistence length. Therefore, these networks can be regarded as stochastic fractal elastic media over the respective range of scales. This implies that no scale decoupling exists and no representative volume element can be identified on scales below the upper correlation cut-off scale.
KeywordsFractals Homogenization Stochastic Elasticity Microstructural
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