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

Wyart, M and Liang, H and Kabla, A and Mahadevan, L (2008) A coordination-based approach to elasticity of floppy and stiff random networks. Physical Review Letters, 101. 215501-.

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## Abstract

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 $\delta z<0$, while a stiff network has $\delta z>0$. 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.

Item Type: Article cond-mat.soft cond-mat.soft cond-mat.mtrl-sci UNSPECIFIED Div C > Biomechanics Cron Job 07 Mar 2014 11:59 26 Nov 2014 19:05