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Discrete element approaches
Published in M. Oda, K. Iwashita, Mechanics of Granular Materials, 2020
It has been demonstrated by various researchers that reasonably good qualitative results, in terms of general trends, can be obtained using assemblies of discs or spheres with simple linear springs to model the normal and tangential interactions between the particles. However, quantitative agreement with experimental data necessitates more sophisticated modelling of the particle properties. Particle shape is of paramount importance as demonstrated by simulations of 2D elliptical systems by Rothenburg & Bathurst (1992), Ting et al. (1993) and 3D simulations of systems of ellipsoidal particles, Lin & Ng (1997). More complex particle shapes may be modelled using superquadrics, Williams & Pentland (1991). An alternative approach to modelling non-spherical particles is to fuse a small number of spheres together, Walton & Braun (1993). It has also been demonstrated by Thornton & Lanier (1997), Thornton & Antony (1998) that, even for polydisperse systems of spheres, the details of the particle-particle interaction rules can have a significant effect on both the quantitative and qualitative behaviour. This is important in process engineering where there is a need to know how the macroscopic mechanical response may be modified by changing the particle specification and particulate materials may be composed of different particle types, e.g. mixtures of hard and soft particles, brittle or ductile particles.
Effects of cylindrical particle properties on pile formation
Published in Particulate Science and Technology, 2023
Xu Tian, Heng Zhou, Junren Qin, Wei Cao, Mingyin Kou, Shengli Wu, Guangwei Wang, Baojun Zhao, Xiaodong Ma
At present, there are three modeling methods used in simulations: multi-sphere models, polyhedral models, and superquadric models. The equations of multi-sphere and polyhedral models are almost the same, but collision detection is more complex in polyhedral models. Combined multi-sphere models only need to consider whether a single ball collides, while in multi-sphere models, the simulation time increases almost linearly with increases in the number of spherical elements. A superquadric model has advantages in simulating models (square, spherical, ellipsoid, cylindrical) in the form of an equation. The simulation time and accuracy are satisfactory but special software may be required. The purpose of this paper is to explore the influences of parameters rather than actual industrial applications. The number of particles is not fixed, and the additional calculation load of a combined ball model is found to be acceptable.
Evaluation of anisotropic small-angle neutron scattering data from metastable β-Ti alloy
Published in Philosophical Magazine, 2018
Pavel Strunz, Jana Šmilauerová, Miloš Janeček, Josef Stráský, Petr Harcuba, Jiří Pospíšil, Jozef Veselý, Peter Lindner, Lukas Karge
Here, x0, y0, z0 are the coordinates of the particle centre and Rx, Ry, Rz are particle ‘radii’ (halves of its size parameters) in x, y and z direction, respectively. The parameter σ defines the particle shape. For σ = 1, it is a sphere (when Rx = Ry = Rz) or an ellipsoid (when Rx = Ry ≠ Rz or Rx ≠ Ry ≠ Rz). For σ < 1, such shapes are generally termed superquadrics. The particle becomes cube with rounded edges and corners when σ decreases towards zero. In the limit (σ −> 0), the particle is a cube (when Rx = Ry = Rz) or a rectangular prism (when Rx = Ry ≠ Rz or Rx ≠ Ry ≠ Rz). An octahedron can be obtained for σ = 2, and a particle with sharp streaks in the axial directions arises for σ > 2. Therefore, the shape of the particle can be simply changed by changing the parameter σ and the relations between Rx, Ry and Rz (for the change to rod-like or plate-like objects and prolate/oblate ellipsoids). This shape-modelling formula (Equation (1)) was applied to individual particles in both old and new microstructure model.