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arXiv · 2405.19908

Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition

Surajit Chakraborty·Kabir Ramola
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Abstract

We explore the behavior of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic $p^2$ dependence of the correlations as the pressure $p$ approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.

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Surajit Chakraborty, Kabir Ramola. 2024-05-30. Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition. https://doi.org/10.1039/d4sm00328d

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