Advanced strategies for discrete simulations with three-dimensional R-shapes in rockable framework

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.