Duc-Hanh Nguyen

Bonded-cell model for particle fracture

Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.

Evolution of particle size distributions in crushable granular materials

By means of the contact dynamics method together with a particle fracture model, in which the particles are cohesive aggregates of irreducible polygonal fragments, we investigate the evolution of particle size distribution in the process of uniaxial compaction of granular materials. The case of single particle breakup under compressive stress is used to test the method and the influence of discretization (number of irreducible fragments). We show that the breaking threshold of the granular assembly scales with the internal cohesion of the particles but it depends also on the initial size distribution and irregularity of polygonal particle shapes. The evolution of size distribution proceeds by consecutive periods of intense particle crushing, characterized by local shattering instability, and periods of little breaking activity. Starting with either monodisperse or power-law distribution of particle sizes, the latter evolves towards a broad distribution of the fragmented particles with a nearly power-law distribution in the range of intermediate particle sizes. Interestingly, a finite number of large particles survive despite ongoing crushing process due to the more homogeneous distribution of forces in the presence of small fragmented particles filling the pores between larger particles.

Rheology of granular materials composed of crushable particles

Abstract.We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.Graphical abstract

Numerical Modeling of Particle Breaking Process in Granular Materials: Compaction and Evolution of Size Distribution

The compaction of powders depends both on grain rearrangements and grain breakage. We introduce a grain fracture model prescribed in the framework of the contact dynamics method for the simulation of uniaxial compaction. We find that the grain size reduction is highly heterogeneous as a consequence of inhomogeneous stress transmission as observed in real grinding processes or in natural degradation of geomaterials. Even under high stresses, a significant fraction of grains survive whereas many grains are fully shattered. The grain size distribution tends to a power-law distribution with increasing size span. We analyze the progressive evolution of compressibility during compaction as well as the effect of grain shape and size distribution.