Stress Response of Jammed Solids: Prestress and Screening
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909794249474048 |
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| author | Chakraborty, Surajit Nampoothiri, Jishnu N. Bhattacharjee, Subhro Chakraborty, Bulbul Ramola, Kabir |
| author_facet | Chakraborty, Surajit Nampoothiri, Jishnu N. Bhattacharjee, Subhro Chakraborty, Bulbul Ramola, Kabir |
| contents | Unlike classical elasticity, where stresses arise from deformations relative to a stress-free reference configuration, rigidity in amorphous systems is maintained by disordered force networks that generate internal prestress. Previously, we introduced a ''stress-only'' formulation, where mechanical equilibrium resembles Gauss's law in a rank-2 tensor electrostatics with vector charges, and demonstrated that the mechanical response of jammed solids is described by the dielectric response of this gauge-theoretic formulation. Here, we extend this framework by incorporating scale-dependent screening that captures both dielectric and Debye-type behaviour. This introduces a characteristic length scale in stress correlations as well as in the response to external forces. Through numerical simulations of soft-sphere packings, we show that this length scale is set by the particle size, thus providing a natural ultraviolet cutoff while preserving long-wavelength emergent elasticity. We show that this lengthscale remains finite for all pressures, with no evidence for an emergent Debye-like screening near the frictionless unjamming transition. We demonstrate that although individual realisations show strong fluctuations, disorder averaging at fixed macroscopic conditions yields a robust dielectric-like response that persists up to unjamming. Finally, we also provide a physical interpretation of the gauge field within the electrostatic mapping: relative grain displacements in response to localised external perturbations correspond to difference in the gauge field, linking the field-theoretic description to particle-level mechanics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stress Response of Jammed Solids: Prestress and Screening Chakraborty, Surajit Nampoothiri, Jishnu N. Bhattacharjee, Subhro Chakraborty, Bulbul Ramola, Kabir Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics Unlike classical elasticity, where stresses arise from deformations relative to a stress-free reference configuration, rigidity in amorphous systems is maintained by disordered force networks that generate internal prestress. Previously, we introduced a ''stress-only'' formulation, where mechanical equilibrium resembles Gauss's law in a rank-2 tensor electrostatics with vector charges, and demonstrated that the mechanical response of jammed solids is described by the dielectric response of this gauge-theoretic formulation. Here, we extend this framework by incorporating scale-dependent screening that captures both dielectric and Debye-type behaviour. This introduces a characteristic length scale in stress correlations as well as in the response to external forces. Through numerical simulations of soft-sphere packings, we show that this length scale is set by the particle size, thus providing a natural ultraviolet cutoff while preserving long-wavelength emergent elasticity. We show that this lengthscale remains finite for all pressures, with no evidence for an emergent Debye-like screening near the frictionless unjamming transition. We demonstrate that although individual realisations show strong fluctuations, disorder averaging at fixed macroscopic conditions yields a robust dielectric-like response that persists up to unjamming. Finally, we also provide a physical interpretation of the gauge field within the electrostatic mapping: relative grain displacements in response to localised external perturbations correspond to difference in the gauge field, linking the field-theoretic description to particle-level mechanics. |
| title | Stress Response of Jammed Solids: Prestress and Screening |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2509.14336 |