Microstructure and micromechanics of polydisperse granular materials: Effect of the shape of particle size distribution Joanna Wiącek ⁎ ,1 , Marek Molenda 1 Institute of Agrophysics, Polish Academy of Sciences, Doswiadczalna 4, 20-290 Lublin 27, Poland abstract article info Article history: Received 4 April 2014 Received in revised form 7 July 2014 Accepted 14 August 2014 Available online 23 August 2014 Keywords: Particle size distribution Discrete element method Microstructure Micro-mechanics The uniaxial compression of polydisperse spheres with continuous: normal, log-normal, arbitrary and discrete uniform particle size distribution was modelled with the discrete element method (DEM). The evolution of solid fraction, coordination number and fabric tensor with increasing compressive stress was investigated in granular packings of equal mean particle diameter and standard deviation of particle mean diameter. The study of the relationship between the shape of particle size distribution and the micromechanical properties of granular packings included the determination of the contact forces and the degree of mobilisation of friction in contacts between particles. Slight influence of the shape of continuous particle size distribution on the solid fraction and coordination number in polydisperse packings was observed. The discrete uniform distribution provided the number of contacts lower by 7% as compared to continuous distribution. Concerning the mobilisation of friction in contacts between spheres, the average ratio of the tangential: normal contact forces in packing with discrete distribution was 25% higher than the one calculated for normal particle size distribution. © 2014 Elsevier B.V. All rights reserved. 1. Introduction The polydispersity of particulate system is one of the physical attributes of granular materials which determine their fabric and micromechanics [1–3]. The term fabric denotes the physical constitution of a granular material as expressed by the spatial arrangement of the particles and associated voids [4] which is of great importance in many branches of science and technology. Many scientific papers dealing with the microstructure of packings of ideal uniformly sized spheres have been published over the past several decades [5–7], however the most particle packings involved in the industrial and natu- ral processes are composed of a broad range of particle sizes. The degree of particle size heterogeneity was found to determine the geometrical and micromechanical properties of packings, which in turn strongly affected their mechanical response to shear [1] or compaction [8,9] as well as the segregation and flow of particle mixtures during mixing [10] and discharge processes [11]. In general, the research on polydisperse particulate systems focused on the study of relationship between degree of polydispersity of packings and their mechanical properties [1,3]. The particle size distribution may be described by various distribution functions which were reported to determine porosity and coordination number in granular packings [12–14]. In the majority of investigations carried out in that field the Gaussian (normal) or log-normal particle size distributions were applied [15–17]. These two distributions are most often assumed to describe the random variation that occurs in the data from many scientific disciplines [18–20], however other distributions, such as exponential, arbitrary, bimodal, uniform or Rossin–Rammler may be also applied to describe the particle size distribution in particulate systems [13,15]. Understanding the relationship between particle size distribution and micromechanical properties of granular packings is of high importance to many branches of industry in which granular materials are processed, e.g. pharmaceutical, chemical, building or ceramics industry. Micro- structure characterization of particulate media is critical to understand and predict their macromechanical response to loads applied during mechanical processes that in turn affects efficiency of the process as well as quality and safety of products. Due to insufficient knowledge on the microstructure and micromechanical properties of particulate assemblies, resulting from limitations of experimental methods, computational approaches are increasingly preferred to represent granular media. In mechanics and physics, the description and modelling of heterogeneous particulate materials such as powders or grains may be done in two ways [21]. The first one, based on continuum theory, relies on empirical assump- tions about the macroscopic material behaviour and involves stress, strain and plastic yield conditions. In the second approach, the macroscopic analysis is complemented by a microscopic description of the material in which individual particles and their interactions are modelled. Although both approaches have gained widespread applica- tion in the physics and mechanics of granular materials [22–25] the micromechanical approaches, which take into account the Powder Technology 268 (2014) 237–243 ⁎ Corresponding author. E-mail addresses: jwiacek@ipan.lublin.pl (J. Wiącek), mmolenda@ipan.lublin.pl (M. Molenda). 1 Tel.: +48 81 744 50 61. http://dx.doi.org/10.1016/j.powtec.2014.08.020 0032-5910/© 2014 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec