Elasticity of floppy and stiff random networks

M. Wyart, H. Liang, A. Kabla, L. Mahadevan

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We study 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 (average number of springs per node) relative to that of a marginally rigid network δz: a floppy network has δz<0, while a stiff network has δz>0. Under the influence of an externally applied load, we observe that the response of both floppy and stiff networks is controlled by the critical point corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the heterogeneity of the response, and the network stiffening as a function of δz and derive these theoretically, thus allowing us to predict aspects of the mechanical response of glasses and fibrous networks.

    Original languageEnglish (US)
    Article number215501
    JournalPhysical Review Letters
    Volume101
    Issue number21
    DOIs
    StatePublished - Nov 19 2008

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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