Interface Stress Element Method, Rigid Body Spring Model and Applied Element Method

Abstract

Abstract Interface Stress Element Method(ISEM), Rigid Body Spring Model(RBSM) and Applied Element Method(AEM) are typical connected discrete element methods derived from the same origin. Although there are many differences in their model compositions, expression forms, development paths and application situations, the three methods are closely related. In this paper, the commonalities and differences among ISEM, RBSM and AEM were expounded from five aspects: model composition, stiffness matrix for interface, formula for inter-element stress, theoretical system and analysis procedure. They discretize the domain with rigid blocks, but connect them using interface layers, distributed spring pairs and multiple spring pairs respectively. For homogeneous isotropic materials, the stiffness matrixes for RBSM are equal to that for ISEM, and there are only four items different in the stiffness matrix for AEM. The formula for inter-element stress of RBSM and AEM can be expressed by that for ISEM. The relationships among ISEM, RBSM and AEM were further clarified. RBSM and AEM are both special cases of ISEM. They can be incorporated into the theoretical system of Interface Stress Element Method. The three constitute a unified method family.