Smoothed particle hydrodynamics simulation of granular system under cyclic compressions

Abstract

The response of two-dimensional frictionless granular material to isotropic cyclic compression is simulated using an improved version of the Smoothed Particle Hydrodynamics (SPH) method, which includes realistic constitutive model for deformation of individual grains. The study reveals the evolution of mean coordination number and global pressure over cycles. The probability distribution function (PDF) of contact forces for different compression cycles is also reported. The global pressure at maximum compression shows downward trend for packing fractions below a certain value. The structural rearrangement that can give rise to such stress relaxation is studied by mapping relative particle mobilities and quantifying dynamic heterogeneity using a four-point susceptibility measure. The four-point susceptibility measure reveals length and time scales that can characterize the dynamics of driven system. Meso-scale structural rearrangement is studied using Falk-Langer measure of affine and non-affine deformation. The affine and non-affine deformations drop to a stable value and oscillates around it, which suggest that the structure is driving towards a more stable configuration. A negative correlation is found between the local packing fraction and the non-affine squared displacement. Finally, a complex network analysis is employed to better understand the structural rearrangement at meso-scale. The average degree and average clustering coefficient obtained from the complex network analysis show peaks at maximum compressions, but the peak values increase with cycles. The degree per particle is found to be positively correlated with local packing fraction and negatively correlated with the non-affine squared deformation. An enrichment of three-cycle population is seen, suggesting it as the most preferred conformation for particles at the meso-scale.