Compressibility in rigid grains is the physical mechanism responsible for thin layer stability and a fundamental source of non-localities

Granular systems exhibit complex behavior such as self organized criticality, phase transitions, and non-local interactions. Despite such complexities, a variety of continuum-mechanics approaches have been successfully applied to describe granular rheology in specific applications. However, their more general application is hindered by non-local effects that are currently poorly predicted. This is particularly illustrated by the widely observed thin layer stability problem. Thin layer stability manifests clearly in inclined planar granular flow where the critical angle of the system is dependent on the height of granular material. Such effects have even been observed in systems of frictionless grains (Perrin et al 2021), emphasizing a mechanism solely reliant on system geometry and particle contact structures. Our work suggests that the inability of current approaches to capture such effects lies in the reliance on bulk flow descriptions, such as the inertial number, which typically neglects rigidity/deformation of individual grains as a relevant physical parameter. Using a linear dashpot model and numerical methods to simulate the collisions of deformable grains, we show that the dynamics are sensitive to system size, especially when system-scale lengths are comparable to particle diameter. This sensitivity is introduced through a deformation based physical mechanism where compressed chains of particles alter the energy needed to escape from the gravity well between two particles. Since this energy threshold is a critical point between two steady states of the system, small perturbations cause large system wide effects. Finally we show that by using our proposed compressibility based physical mechanism to account for these changes in this critical point, we recover the experimentally observed scaling of thin layer stability.