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.
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY - Paternité
Licence : CC BY - Paternité