Stiffening of under-constrained spring networks under isotropic strain
We study strain stiffening of sub-isostatic spring networks, numerically testing analytical predictions of the elastic network properties, e.g., a linear scaling of the shear modulus with isotropic tension. We also probe how our results depend on system size. Disordered spring networks are a useful paradigm to examine macroscopic mechanical properties of amorphous materials. Here, we study the elastic behavior of under-constrained spring networks, i.e. networks with more degrees of freedom than springs. While such networks are usually floppy, they can be rigidified by applying external strain. Recently, an analytical formalism has been developed to predict the scaling behavior of the elastic network properties close to this rigidity transition. Here we numerically show that these predictions apply to many different classes of spring networks, including phantom triangular, Delaunay, Voronoi, and honeycomb networks. The analytical predictions further imply that the shear modulus G scales linearly with isotropic stress T close to the rigidity transition. However, this seems to be at odds with recent numerical studies suggesting an exponent between G and T that is smaller than one for some network classes. Using increased numerical precision and shear stabilization, we demonstrate here that close to the transition a linear scaling, G ∼ T, holds independent of the network class. Finally, we show that our results are not or only weakly affected by finite-size effects, depending on the network class.
- Pub Date:
- July 2022
- Condensed Matter - Soft Condensed Matter;
- Condensed Matter - Materials Science
- 17 pages, 10 figures