Two-dimensional Metal Particles Pile Resistor Network Model Algorithm And The Fluctuation Study

Granular materials have many special properties and characteristics of motion. They represent both solid-like and liquid-like features, and exhibit rich phenomena of nonlinear dynamics. They have complex mechanical properties and electrical properties and people have not formed uniform views and theories yet. Researches on the conductivity of metallic beads have been proceed based on the mechanical model such as q model or Scalar Arching Model, but they show great differences and conclusion between models and experiments. This article developed a new transformation algorithm applied to the resistor network and found the simulation calculation is almost the same with the real experiments based on the electrical model.In this paper, we developed a new electrical model to describe two-dimensional metallic beads. First, we developed a new transformation algorithm to calculate the resistance between two arbitrary nodes in a two-dimensional random resistor network. Through the second-order method of finite difference, the symmetrical characteristic in the network and the analysis time complexity, we proved our algorithm accurate and efficient. Then, we reduced the two-dimensional metallic beads to a two-dimensional random resistor network, set all kinds of network parameters and through transforming algorithm we calculated how the size of network and width of random resistor influenced the resistance and its fluctuation distribution; we generated a Gauss-Distribution to do the same search. At last we simulated the electrical fluctuation in two-dimensional metallic beads under mechanical perturbation such as knocking and found an exponential law and inverse correlation by using our own network model. Therefore, we compared the simulation results to the experimental results and they were consilient.We can simulate more electrical experiments about metallic beads rely on the algorithm we developed, such as the resistance fluctuation under heat perturbation, and the resistance fluctuation under different geometries and so on. Thus, the algorithm and theory model we developed can be a very good reference for studying the electrical properties in metallic beads.