Energy-Conserving Contact Dynamics of Nonspherical Rigid-Body Particles

TL;DR

This work presents an energy-conserving contact-dynamics framework for convex nonspherical rigid bodies, combining 2D vertex–boundary and 3D vertex–surface/edge–edge contact detections with a continuous normal and tangential force model to prevent overlap while conserving total energy during translation and rotation. Implemented in LAMMPS, the approach retains duplicate contact pairs to ensure force continuity and scalability, enabling accurate simulations of 2D polygons and 3D polyhedra across packing, diffusion, and equation-of-state studies. Thorough 2D and 3D validations show stable energy, shape-dependent diffusion, and crystallization tendencies consistent with reference hard-particle data, demonstrating the method’s capacity to capture nonequilibrium dynamics in complex anisotropic systems. The framework provides a robust platform for exploring colloidal self-assembly, granular flow, and hydrodynamic interactions in systems of convex nonspherical particles, with future directions including surface heterogeneity and coupling to hydrodynamics.

Abstract

Understanding the contact dynamics of nonspherical particles beyond the microscale is crucial for accurately modeling colloidal and granular systems, where shape anisotropy dictates structural organization and transport properties. In this paper, we introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles, integrating vertex-boundary interactions in 2D with vertex-surface and edge-edge detection in 3D. This formulation enables continuous force evaluation and strictly prevents particle overlap while conserving total energy during translational and rotational motion. Simulations of polygonal and polyhedral particles confirm the framework's stability and demonstrate its capability to capture packing behavior, anisotropic diffusion, and equations of state. The framework establishes a robust and extensible foundation for investigating the nonequilibrium dynamics of complex nonspherical particle systems, with potential applications in colloidal self-assembly, granular flow, and hydrodynamics.

Figures (7)

• Figure 1: Scheme of contact forces and interactions. The contact force is determined by the interparticle distance: a repulsive force arises when the separation $d$ is smaller than the combined skin layer thickness $(R_i + R_j)$, while the cutoff distance $r_c$ switches on the attractive force for separations beyond $R_i + R_j$. Vertex-boundary interactions in 2D (a triangle and a square) involve 7 ($3+4$) pairs, while in 3D, vertex-surface interactions for a tetrahedron and a cube involve 12 ($4+8$) pairs, and edge-edge interactions involve 72 ($6 \times 12$) pairs.
• Figure 2: Energy evolution for various 2D shapes, including triangles, squares, pentagons, and hexagons. The simulation cycles through NPT for $20\tau$ and NVE for $20\tau$ at $T^* = 1$ and target pressures $P^* = 1, 3, 6, 7, 8,$ and $10$.
• Figure 3: Averaged radial distribution functions $g(r)$ and angular distribution functions $g(\theta)$ for 2D particles with triangular, square, pentagonal, and hexagonal shapes at various packing fractions $\eta$. Scaled perfect tessellation $g(r)$ curves are shown in red for comparison.
• Figure 4: Energy evolution for a mixed system of 3D particles, including cubes, large cubes, tetrahedra, hexagonal prisms, and rods, with 200 of each shape. The simulation cycles through NPT for $20\tau$, NVT for $20\tau$, and NVE for $40\tau$ at target pressures $P^* = 0.2, 1, 2, 4,$ and $10$, and temperature $T^* = 1.5$.
• Figure 5: Laboratory-frame translational diffusion, $D_{\mathrm{T}}^{\mathrm{Lab}}$, and body-frame translational, $D_{\mathrm{T}}^{\mathrm{Body}}$, and rotational, $D_{\mathrm{R}}^{\mathrm{Body}}$, diffusion as a function of the total packing fraction $\eta$ for cubes, large cubes, tetrahedra, hexagonal prisms, and rods (see Fig. \ref{['fig:diff_eng']}). Body-frame diffusion of anisotropic particles is evaluated along the basal and axial axes for hexagonal prisms and along the transverse and longitudinal axes for rods.