2024/05/30 by Surajit Chakraborty, Kabir Ramola, Chakraborty, Surajit +1
Engineering · Materials Science · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Material Properties and Failure Mechanisms #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2405.19908
openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 p2 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.