### 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 language | English (US) |
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Article number | 215501 |

Journal | Physical Review Letters |

Volume | 101 |

Issue number | 21 |

DOIs | |

State | Published - Nov 19 2008 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*101*(21), [215501]. https://doi.org/10.1103/PhysRevLett.101.215501

**Elasticity of floppy and stiff random networks.** / Wyart, M.; Liang, H.; Kabla, A.; Mahadevan, L.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 101, no. 21, 215501. https://doi.org/10.1103/PhysRevLett.101.215501

}

TY - JOUR

T1 - Elasticity of floppy and stiff random networks

AU - Wyart, M.

AU - Liang, H.

AU - Kabla, A.

AU - Mahadevan, L.

PY - 2008/11/19

Y1 - 2008/11/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=56849112493&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevLett.101.215501

DO - 10.1103/PhysRevLett.101.215501

M3 - Article

VL - 101

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 21

M1 - 215501

ER -