Investigation of a boundary simulation of continuity using the discrete solid element method

Abstract

The discrete solid element method is an efficient numerical method that simulates the large deformation, strong material nonlinearity, fracture, and dynamic problems of continuity. In the discrete solid element method model, the spring stiffness of the spherical elements on the boundary is different from that inside the discrete solid element method model based on the principle of conservation of energy. The spring stiffness of the spherical elements on the boundary of the discrete solid element method model is shown to have a significant effect on the macroscopic properties. According to the position of the spherical elements on the boundary of the discrete solid element method model, the spherical elements on the boundary are divided into three types, which are spherical elements on the surface position, on the edge position, and on the corner position. To accurately reflect the mechanical behavior of the material, the principle of energy conservation is used to strictly deduce the spring stiffness of the three types of spherical elements on the boundary, and the relationship between the spring stiffness and elastic constants is established. The numerical example shows that the calculation accuracy of the discrete solid element method in modeling the mechanical behavior of continuity is improved after the spring stiffness of the spherical elements on the boundary is revised. In addition, the applications of the discrete solid element method to dynamic buckling of the thin plate and buckling of the cracked thin plate are also given.