Linking microscopic and macroscopic response in disordered solids

Abstract

The modulus of a rigid network of harmonic springs depends on the sum of the energies in each of the bonds due to the applied distortion: compression in the case of the bulk modulus, $B$, or shear in the case of the shear modulus, $\mathcal{G}$. The distortion need not be global and we introduce a local modulus, $L_i$, associated with changing the equilibrium length of a single bond, $i$, in the network. We show that $L_i$ is useful for understanding many aspects of the mechanical response of the entire system. For example, it allows an understanding, and efficient computation, of how each bond in a network contributes to global properties such as $B$ and $\mathcal{G}$ and sheds light on how a particular bond's contribution to one modulus is, or is not, correlated with its contribution to another.

7 pages, 6 figures

References in corpus (5)

• Fractal free energy landscapes in structural glasses
• Jamming Criticality Revealed by Removing Localized Buckling Excitations
• Non-affine response: jammed packings versus spring networks
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• Tunable failure: control of rupture through rigidity

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