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Pré-Publication, Document De Travail Année : 2023

Partition sum of thermal, under-constrained systems

Résumé

Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain. Following our recently-developed analytical theory for the athermal limit, here and in the companion paper, we extend this theory to under-constrained systems at finite temperatures close to the athermal transition point. We derive from first principles the partition sum for a broad class of under-constrained systems, from which we obtain analytic expressions for elastic material properties such as isotropic tension $t$ and shear modulus $G$ in terms of isotropic strain $\varepsilon$, shear strain $\gamma$, and temperature $T$. Our work unifies the physics of systems as diverse as polymer fibers & networks, membranes, and vertex models for biological tissues.
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Dates et versions

hal-04251711 , version 1 (20-10-2023)

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Cheng-Tai Lee, Matthias Merkel. Partition sum of thermal, under-constrained systems. 2023. ⟨hal-04251711⟩
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