Stress Response of Granular Systems

Abstract

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of contact forces between constituent grains on a given, disordered, contact network, to external perturbations. By mapping this response to the spectral properties of the graph Laplacian corresponding to the underlying contact network, we show that this naturally leads to spatial localization of forces. We present numerical evidence for localization using exact diagonalization studies of network Laplacians of soft disk packings. Finally, we discuss the role of other constraints, such as torque balance, in determining the stability of a granular packing to external perturbations.

21 pages, 10 figures

References in corpus (2)

• Effects of Friction and Disorder on the Quasi-Static Response of Granular Solids to a Localized Force
• Scaling Theory for the Frictionless Unjamming Transition

Cited by in corpus (10)

• Network Analysis of Particles and Grains
• Emergent Elasticity in Amorphous Solids
• Microscopic origin of frictional rheology in dense suspensions: correlations in force space
• Protocol-Dependence and State Variables in the Force-Moment Ensemble
• Athermal fluctuations in disordered crystals
• Response evolution of mechanical metamaterials under architectural transformations
• Investigating the Nature of Discontinuous Shear Thickening: Beyond a Mean-Field Description
• Force networks, torque balance and Airy stress in the planar vertex model of a confluent epithelium
• Couple stresses and discrete potentials in the vertex model of cellular monolayers
• Long-range correlations in pinned athermal networks