3D Discrete Solid-Element Method for Elastoplastic Problems of Continuity

Abstract

This paper proposes a novel three-dimensional (3D) discrete solid-element method (DSEM) to calculate the extremely large deformation and high material nonlinearity of continuity. In DSEM, the material is discretized into rigid spherical elements. The two spherical elements on the edge and the diagonal line of the cube model are linked together through springs, which consist of one normal spring and two shear springs. The mechanical behavior of the structure is calculated using the discrete grid system composed of spherical elements and springs. To accurately reflect the mechanical behavior of the material, the principle of energy conservation is used to strictly deduce the spring stiffness, and the relationship between spring stiffness and elastic constants is established. In accordance with the plastic mechanics and the fourth strength theory of the material, the yield equation and elastoplastic force-displacement equations in DSEM are deduced based on the orthogonal flow rule and the consistency condition. The numerical analysis shows that DSEM can effectively address the problems of extremely large deformation and high material nonlinearity.