Résumé
The Discrete Element Method (DEM) is widely used to simulate the mechanical behavior of granular materials across a broad range of applications and industrial domains. Particle shape is a key feature playing a crucial role for physics-fidelity of DEM simulations. However, accurately representing complex particle shapes within DEM frameworks presents significant challenges such as defining unambiguous contact normals or managing geometric singularities. Rigid particles are often modeled as convex polyhedra, which inherently suffer from ill-defined outward normal vectors at sharp edges and vertices. To represent non-convex geometries, these polyhedra must typically be combined, further increasing the computational and geometric complexity. In this work, we adopt an efficient and robust strategy to overcome these limitations by using R-shapes, defined as rounded-edge shapes, also known as sphero-polyhedra, obtained by sweeping a sphere of radius R along the edges and faces of a base polyhedral shape. This construction results in smooth surface transitions and circumvents common issues associated with traditional polygonal representations. This paper provides a detailed presentation of the implementation, structure, and advantages of R-shapes in DEM simulations. The proposed solutions are implemented in a fully open-source software package called Rockable, developed in C++, which integrates state-of-the-art numerical techniques and shared-memory parallelization for enhanced performance. Beyond the geometric modeling aspects, we also address several methodological challenges, including the treatment of contact elasticity and the numerical integration scheme. The combined contributions of this work offer a practical and efficient framework for simulating complex particle shapes in DEM with high physics fidelity and computational efficiency.Program summary
Program Title:Rockable
CPC Library link to program files: (to be added by Technical Editor)
Developer’s repository link:
https://github.com/richefeu/rockable
Licensing provisions: CeCILL-B
Programming language:C++11
Supplementary material:
Nature of problem(approx. 50–250 words):
The open-source software Rockable addresses key challenges in simulating the mechanical behavior of granular materials using the Discrete Element Method (DEM), widely applied in both industrial applications and academic studies particularly where particle shape plays a critical role. Accurate modeling of the diversity of particle shapes in DEM remains non-trivial, due in part to ambiguities in defining contact normals. Rigid particles are often represented as convex polyhedra, which suffer from poorly defined outward normals at edges and vertices. Additionally, modeling non-convex shapes typically requires aggregating multiple convex elements, increasing complexity. Rockable resolves these issues through the use of R-shapes, or sphero-polyhedra, obtained by sweeping a sphere of radius R along the edges and faces of a polyhedral base. Developed in C++, Rockableintegrates state-of-the-art numerical techniques and supports shared-memory parallelism for high-performance simulations. It also addresses key physical modeling challenges, including contact elasticity and particle breakage.
Solution method(approx. 50–250 words):
Rockable implements a geometry-based contact detection algorithm for R-shapes, relying on the classification of contacts into four elementary types: vertex-vertex, vertex-edge, vertex-face, and edge-edge. This systematic approach provides a unified framework for computing contact points and their associated local frames. A key advantage of this method is its ability to reduce complex contact scenarios, such as face-face interactions, into combinations of these fundamental cases. This modular treatment not only improves robustness and computational efficiency but also extends naturally to non-convex and hollowed shapes. The framework is designed to be extensible, making Rockable a versatile tool for DEM-based modeling of irregular and evolving particle geometries.