Discrete element simulation of particles defined by cardioids

Discrete element method with different shapes has attracted considerable research attentions because particle shapes affect dynamic properties of the system. Although convex particles have been extensively investigated, studies on concave particles are limited. Cardioid particles are constructed in this study using parametric equation. Multi-point contact detection algorithm and calculation methods of geometric parameters, such as normal vector, curvature, and overlapping at the contact point, are provided. Two-dimensional (2D) and three-dimensional (3D) systems are simulated by using the discrete element method. Convergence of energy in falling process under gravity verifies the stability and correctness of the algorithm. On this basis, shear curves of simple shear tests with different shapes are calculated and propagation processes of elastic waves in uniaxial compression systems with periodic boundary conditions are simulated. Results showed that the particle shape affects not only shear strength of the simple shear system but also elastic wave velocity in the uniaxial compression system. The particle shape will cause anisotropies of normal vector of contact force, branch vector, and contact force distributions. Influence of shape on the wave velocity is explained from the perspective of anisotropy. The proposed method in this study is universal and suitable for other shapes defined by different parametric equations and can be used to investigate dynamic properties of particle systems with various shapes.