A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic n...

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Bibliographic Details
Published in:arXiv.org 2008-06
Main Authors: Wyart, M, Liang, H, Kabla, A, Mahadevan, L
Format: Article
Language:English
Subjects:
Computer simulation
Critical point
Elasticity
Mathematical models
Mechanical analysis
Shear modulus
Springs (elastic)
Stiffening
Two dimensional models
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Summary:We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network \(\delta z\); a floppy network has \(\delta z0\). Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of \(\delta z\), derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.
ISSN:2331-8422
DOI:10.48550/arxiv.0806.4571