A novel discrete element method based on the distance potential for arbitrary 2D convex elements

Abstract

Summary A new 2‐dimensional discrete element method, which is able to simulate a system involving a large number of arbitrary convex elements, is proposed. In this approach, a novel distance potential function is defined using a normalized format of the penetrated distance between contact couples, while a holonomic and precise algorithm for contact interaction is established, accounting for the influence of the tangential contact force. Furthermore, the new contact detection algorithm is well suited for nonuniform blocks unlike the common no binary search method that requires uniform elements. The proposed method retains the merit of the combined finite‐discrete element method and avoids its deficiencies. Compared with the existing finite‐discrete element method, the distance potential function has a clear physical meaning, where the calculation of contact interaction avoids the influence of the element shape. Accordingly, the new method completely gets rid of the restraint of uniform element type and can be applied to arbitrary convex elements. The new method is validated with well‐known benchmark examples, and the results are in very good agreement with existing experimental measurement and analytical solutions. Finally, the proposed method is applied to simulate the Tangjiashan landslide.

A resolved CFDEM method for the interaction between the fluid and the discontinuous solids with large movement

“…30 For the simulation of FSI-D problems with large movement of the solids, the optimal choice is combining the computational fluid dynamics (CFD) with the discontinuous methods, for instance, the discrete element method (DEM). 31 A significant attempt is the establishment of the CFD-DEM (CFDEM) methods, [32][33][34][35] in which the simulation of the coupling between the fluid and the discontinuous solids with arbitrary large movement is accomplished. However, the FSI force in the CFDEM methods is simplified as the drag force determined by the void fraction, and the common empirical formulas were provided by Ergun 36 or Di Felice.…”

“…For the simulation of FSI‐D problems with large movement of the solids, the optimal choice is combining the computational fluid dynamics (CFD) with the discontinuous methods, for instance, the discrete element method (DEM) . A significant attempt is the establishment of the CFD‐DEM (CFDEM) methods, in which the simulation of the coupling between the fluid and the discontinuous solids with arbitrary large movement is accomplished.…”

A robust potential-based contact force solution approach for discontinuous deformation analysis of irregular convex polygonal block/particle systems

“…The concept of ''contact potential'' is initially proposed by [28] in their work on penalty function method for combined finite-discrete element method, and it is used for contact force computation among triangles and tetrahedrons. The definition of potential has been improved for triangles [49], convex polygons [56], convex polyhedra [57], concave polygons [7], and irregular polyhedra [65]. The finite element topology was also applied to construct a smooth potential field in FDEM simulations [17].…”

“…The potential-based penalty function approach [28] provides a robust framework for contact force computation of two contacting bodies. Some recent improvements include the redefined potential function for triangles with clear physical meaning [49], the improved distance potential for convex polygons [56], concave polygons [7] and convex polyhedra [57], the potential traction based on triangle meshes [47] and tetrahedral element [48], robust potential function for irregular polyhedra [65], and the smooth contact algorithm [17]. In this paper, the original contact potential-based penalty function method [28] is improved to be suitable for polygons with small edges, small angles, or small faces.…”

Modified predictor‐corrector solution approach for efficient discontinuous deformation analysis of jointed rock masses

“…Uncertainty in the contact normal direction exists in some v-v types, which has been discussed in Bao and Zhao 45,46 and Fan and He. 47 Moreover, the contact theory 48 and energy-conserving contact interaction models 49 provided frameworks for solving the contact problems, while the corner rounding strategy, 44 the contact potential method 50 and its improved versions [51][52][53] have been successfully applied to resolve this singularity issue.…”