| Issue |
EPL
Volume 148, Number 6, December 2024
|
|
|---|---|---|
| Article Number | 61002 | |
| Number of page(s) | 7 | |
| Section | Statistical physics and networks | |
| DOI | https://doi.org/10.1209/0295-5075/ad9a74 | |
| Published online | 23 December 2024 | |
On inequalities of shear modulus contributions in disordered elastic bodies
1 Université de Strasbourg & CNRS, Institut Charles Sadron - 23 rue du Loess, 67034 Strasbourg, France
2 Université de Lorraine, LCP-A2MC - 1 Bd Arago, 57070 Metz, France
Received: 2 October 2024
Accepted: 4 December 2024
We investigate generic inequalities of various contributions to the shear modulus μ in ensembles of amorphous elastic bodies. We focus first on a simple elastic network model with connectivity matrices (CMs) which are either annealed or quenched, at or out of equilibrium. The stress-fluctuation formalism relation for μ is rewritten as 
with 
characterizing the variance of the quenched shear stresses and 
being a simple average over all states and CMs. For equilibrium CM distributions becomes equivalent to the shear modulus of annealed systems, i.e., 
, while more generally may become strongly negative as shown by considering a temperature quench and a scalar active two-temperature model. Consistent relations are also found for glass-forming colloids where 
for equilibrium ensembles, i.e., μ is set by the quenched shear stresses, while becomes again negative otherwise.
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