Field theory for mechanical criticality in disordered fiber networks

Sihan Chen; Tomer Markovich; Fred C. MacKintosh

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arXiv · 2310.12383

Field theory for mechanical criticality in disordered fiber networks

Sihan Chen·Tomer Markovich·Fred C. MacKintosh

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Abstract

Strain-controlled criticality governs the elasticity of jamming and fiber networks. While the upper critical dimension of jamming is believed to be $d_u$=2, non mean-field exponents are observed in numerical studies of 2D and 3D fiber networks. The origins of this remains unclear. In this study we propose a minimal mean-field model for strain-controlled criticality of fiber networks. We then extend this to a phenomenological field theory, in which non mean-field behavior emerges as a result of the disorder in the network structure. We predict that the upper critical dimension for such systems is $d_u$=4 using a Gaussian approximation. Moreover, we identify an order parameter for the phase transition, which has been lacking for fiber networks to date.

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Sihan Chen, Tomer Markovich, Fred C. MacKintosh. 2023-10-18. Field theory for mechanical criticality in disordered fiber networks. https://arxiv.org/abs/2310.12383

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