Strain correlation functions in isotropic elastic bodies: Large wavelength limit for two-dimensional systems

Abstract

Strain correlation functions in two-dimensional isotropic elastic bodies are shown both theoretically (using the general structure of isotropic tensor fields) and numerically (using a glass-forming model system) to depend on the coordinates of the field variable (position vector r in real space or wavevector q in reciprocal space) and thus on the direction of the field vector and the orientation of the coordinate system. Since the fluctuations of the longitudinal and transverse components of the strain field in reciprocal space are known in the long-wavelength limit from the equipartition theorem, all components of the correlation function tensor field are imposed and no additional physical assumptions are needed. An observed dependence on the field vector direction thus cannot be used as an indication for anisotropy or for a plastic rearrangement. This dependence is different for the associated strain response field containing also information on the localized stress perturbation

17 pages, 7 figures. arXiv admin note: text overlap with arXiv:2303.16571

References in corpus (4)

• Emergence of long-ranged stress correlations at the liquid to glass transition
• Long-range spatial correlations of particle displacements and the emergence of elasticity
• Correlations of tensor field components in isotropic systems with an application to stress correlations in elastic bodies
• Spatial correlation functions for non-ergodic stochastic processes of macroscopic system

Cited by in corpus (1)

• Isotropic tensor fields in amorphous solids: Correlation functions of displacement and strain tensor fields