Stability and anomalous entropic elasticity of sub isostatic random-bond networks

TL;DR

This paper investigates how thermal fluctuations influence the elasticity of sub-isostatic random-bond networks, revealing anomalous temperature-dependent rigidity and stability below the athermal rigidity transition.

Contribution

It demonstrates that thermal fluctuations stabilize these networks, leading to finite moduli and revealing unique temperature scaling behaviors not observed in athermal conditions.

Findings

Thermal fluctuations induce finite bulk and shear moduli below the athermal transition.

Bulk modulus scales as T^{0.66} below the strain threshold, indicating anomalous entropic elasticity.

Shear modulus exhibits a T^{0.5} scaling at the zero-temperature rigidity point.

Abstract

We study the elasticity of thermalized spring networks under an applied bulk strain. The networks considered are sub-isostatic random-bond networks that, in the athermal limit, are known to have vanishing bulk and linear shear moduli at zero bulk strain. Above a bulk strain threshold, however, these networks become rigid, although surprisingly the shear modulus remains zero until a second, higher, strain threshold. We find that thermal fluctuations stabilize all networks below the rigidity transition, resulting in systems with both finite bulk and shear moduli. Our results show a $T^{0.66}$ temperature dependence of the moduli in the region below the bulk strain threshold, resulting in networks with anomalously high rigidity as compared to ordinary entropic elasticity. Furthermore we find a second regime of anomalous temperature scaling for the shear modulus at its zero-temperature rigidity point, where it scales as $T^{0.5}$, behavior that is absent for the bulk modulus since its athermal rigidity transition is discontinuous.