Particle shape has a huge effect on the behaviour of a bulk material. It is of fundamental importance in packing, affecting the porosity of a static bed of particles and the angle of repose of sand piles [1]. In dynamic systems, variability in particle shape induces segregation [1] and affects flow rates [2]. Temporal changes of particle shape due to attrition, fragmentation or surface abrasion also have important effects. For example, crystals produced in the pharmaceutical sector [3] are often subject to attrition with major implications for product quality, affecting bulk density, specific surface area, segregation behaviour and even surface chemistry [4]. Discrete element method (DEM) simulations have greatly contributed to the analysis of the particle-scale mechanisms that underlie the complexity of the overall material response. However, spheres are generally used to model particles in 3D DEM simulations for computational simplicity and this is often inadequate as particle shape is hugely important.

In order to represent irregular particles, a compact "irregularity function" can be stored for each particle which describes how the shape deviates from a bounding sphere. These functions of angle can be piecewise, and particles thus defined can take almost any form. During the "initialization step" of the simulation, these functions can finely discretised in nodes and the positions of nodes are stored. Contact detection of these irregular particles is conveniently carried out as a hierarchical process [5], where a first coarse-grained approximation of the surface is used to evaluate the "most likely" surfaces in contact. The fine discretization of the surface comes into play only in detailed contact evaluation. Contact evaluation can be done by considering the nodes as micro-asperities. We plan to go beyond the elastic approximation, implementing Hertzian contact mechanics between nodes.

Abrasion and fragmentation can be studied by adopting irregularity functions which can change with time depending on contact force, e.g., a number of nodes (or asperities) may be deemed to fail when a predefined contact force has been exceeded. The nodes are then removed and the irregularity function modified accordingly.

**References**

[1]G. Lu, J.R. Third, and C.R. Müller. Discrete element models for non-spherical particle systems: From theoretical developments to applications. Chemical Engineering Science, 127:425 – 465, 2015.

[2]P. W. Cleary and M. L. Sawley. DEM modelling of industrial granular ﬂows: 3D case studies and the eﬀect of particle shape on hopper discharge. Applied Mathematical Modelling, 26(2):89 – 111, 2002.

[3]E. Kougoulos, C.E. Chadwick, and M.D. Ticehurst. Impact of agitated drying on the powder properties of an active pharmaceutical ingredient. Powder Technology, 210(3):308 – 314, 2011.

[4]C. Hare, M. Ghadiri, and R. Dennehy. Chemical Engineering Science, 66(20):4757 – 4770,2011.

[5]J. R. Williams and R. O’Connor. A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries. Engineering computations, 12(2):185 – 201, 1995.