Complex network analysis of force chain structure for granular materials under loading and unloading conditions

Granular materials are associated with the irreversible behaviors during the loading-unloading-reloading path, the mechanism of which can be analyzed in terms of complex network evolutions. In this paper, the discrete element method is used to conduct triaxial tests for granular materials under the loading-unloading-reloading condition. The macroscopic responses of the granular materials and its corresponding complex network characteristics of different strong contact systems are analyzed. It is found that the macroscopic "hysteresis loop" is formed during the loading-unloading-reloading path of dense granular materials, and the microscopic coordination numbers and clustering coefficients also exhibit irreversible behaviors. Different thresholds are used to classify the strong and weak contact systems for granular materials under different loading and unloading stress states, and the difference in the mesostructure corresponding to each stress state decrease as the threshold increases. The maximum cluster of the strong contact system reaches the limit of percolation when the force threshold falls in a range, and the irreversible behaviors of granular materials can be reflected in the geometric and topological features of strong network during the loading-unloading-reloading path.