Characterization Of Jammed State In Bi-disperse Granular Systems

Jammed state is a common phenomenon in complex granular systems, in which the relationship between the mechanical properties and the geometric structures is very complicated. The critical jammed state in two-dimensional particle system is studied by numerical simulation. The system is composed of 2050 particles with two different radii which distribution is random. There is a looser distribution initially for particles with smaller radius in the given space. When the radii increases, there is a transition from looser state to jammed state happening. The particles-radius ratio ?and the percentage of large particlesBk play main roles in this system, which are discussed in detail based on the statistical analysis of the average contact number,packing fraction and contact type. By analyzing the relationship between the pressure and the packing fraction of the granular system, the critical jammed point applying pressure to the boundary can be find out. Numerical simulation result shows that there is no obvious connection between the average contact number and the percentage of large particles for the case that the particles-radius ratio is less than 1.4. The average contact number approximate to 4 when ?=1.4, which is consistent with previous conclusions. The average contact number firstly decreases and then increases when the percentage of large particles become larger for the case ?(29) 1.4. A minimum value =0.84C? is obtained when 0.5Bk(28). When the percentage of large particles increases, the critical packing fraction decreases first and then increases for the casewith ? < 1.8, but it keeps constant almost for ?(29) 1.8. When the percentage of large particles is close to either 0 or 1, the granular system is approximately mono-disperse.In this case, the average contact number and packing fraction become constants.When the percentage is close to 0.5, the critical average contact number decreases all the time with larger particles-radius ratio, while the critical packing fraction decreases first and then increases. The percentage of large-small contact type is also discussed.The value varies following a quadratic function with the increase of the percentage of large particles, while particles-radius ratio have slight impact to this variation.Specifically, we calculate the percentage of large-small contact type based on probabilistic method, and the result agrees well with simulation results. We give the reason why previous researchers studied the case with ?(28)1:4.1 and 0.5Bk(28) on the basis of results in this paper, and find that the values of ? andBk have no influence on the power-law relation around the critical jammed state.Further research the system of two dimensional particle on a specific diameter ratio and particle size under the condition of geometric relationships between structure and mechanical properties. The results show that with the particle pressure gradually increase the cell area increased gradually smaller pore former cell area the sum remains the same, and the shape of the original cell edge number increases gradually, the shape of the pore former cell edge are gradually reduce the system more stable. Heap on the composition of particles on the critical congestion state of the measured probability density did the statistics. The statistical results show that the pressure and the pore former cell area of probability density at critical congestionstate is uni-modal distribution, and the corresponding average to obtain the maximum;Separation of particles the size of the original cell area did not show certain regularity,but the overall statistics have bi-modal probability distribution.