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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2410.02493 |
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| _version_ | 1866915091550568448 |
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| author | Wittmer, J. P. Xu, H. |
| author_facet | Wittmer, J. P. Xu, H. |
| contents | 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 $μ= μ_1 + μ_a$ with $μ_1 \ge 0$ characterizing the variance of the quenched shear stresses and $μ_a$ being a simple average over all states and CMs. For equilibrium CM-distributions $μ_a$ becomes equivalent to the shear modulus of annealed systems, i.e. $μ_a \ge 0$, while more generally $μ_a$ 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 $μ-μ_1=μ_a=0$ for equilibrium ensembles, i.e. $μ$ is set by the quenched shear stresses, while $μ_a$ becomes again negative otherwise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On inequalities of shear modulus contributions in disordered elastic bodies Wittmer, J. P. Xu, H. Soft Condensed Matter Statistical Mechanics 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 $μ= μ_1 + μ_a$ with $μ_1 \ge 0$ characterizing the variance of the quenched shear stresses and $μ_a$ being a simple average over all states and CMs. For equilibrium CM-distributions $μ_a$ becomes equivalent to the shear modulus of annealed systems, i.e. $μ_a \ge 0$, while more generally $μ_a$ 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 $μ-μ_1=μ_a=0$ for equilibrium ensembles, i.e. $μ$ is set by the quenched shear stresses, while $μ_a$ becomes again negative otherwise. |
| title | On inequalities of shear modulus contributions in disordered elastic bodies |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2410.02493 |