Simulation study on micro and macro mechanical behaviour of sand piles Pradip Roul a, ⁎, Alexander Schinner b a Institute for Numerical Mathematics, Duisburg-Essen University, D-47058, Duisburg, Germany b T-Systems, Dachauer Strasse 665, D-80995, Germany abstract article info Available online 5 August 2010 Keywords: Discrete element method Sand pile Representative volume element Stress Strain Fabric We investigate numerically the micro and macro mechanical behaviour of non-cohesive granular materials, especially in the static limit. To achieve this goal we performed numerical simulations generating two- dimensional “sand piles” from several thousands of convex polygonal particles with varying shapes, sizes and corner numbers, using a discrete element approach based on soft particles. We emphasize that the displacement (strain) fields inside sand piles have not been measured in experiments on sand piles. Averaging is made reproducible by introducing a representative volume element (RVE), the size of which we determine by careful measurements. Stress tensors are studied for both symmetric and asymmetric sand piles in two-dimensional systems, where the particles are dropped from a point source. Furthermore, we determine the fabric tensor inside the sand piles. A surprising finding is the behaviour of the contact density in this kind of heap, which increases where the pressure is at a minimum. The fabric is linearly proportional to the product of the volume fraction and the mean coordination number for a pile consisting of mono- disperse mixture of particles. We observe that the macroscopic stress, strain and fabric tensors are not collinear in the sand piles. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Granular materials are of fundamental importance and high interest to various branches of science and technology such as physics, applied mathematics and mechanics. In recent years, considerable interest in granular materials has been stimulated due to their high technological relevance: many products exist as a granulate at some stage of their processing history. Currently, a large amount of money is spent on the transportation and processing associated with the storage and containment of granular materials. However, about 50% of the money is unnecessarily spent because of problems related to the transport of the material from one part of the factory to another part of the factory. Now, to have a look from another angle, it is often assumed that the side wall of a material container receives a constant force from the granular material inside. The common example of this issue is a model of a silo which is of great concern to various industries such as agricultural, pharmaceutical and mining industries, and all construc- tion-based industries. However, this assumption is wrong, and in the general case, forces are non-uniformly propagated within the material, so they are also non-uniformly distributed at the wall of the silo. In some cases, if the force is much larger in some parts of the container than in other parts, the silo might collapse. For in order to avoid problems such as the collapse or breach of a silo, one can simply increase the thickness of the walls by a generously chosen safety margin, which would be unnecessary if we had the knowledge how to design the silo in a proper way, especially taking into account the expected distribution of forces inside the silo. Therefore, the understanding of the basic physical principles behind the stress distribution in static granular materials is clearly important. A simple example out of a collection of granular arrangements is the static sand pile. The formation of a sand pile is related to the fundamental behaviour of granular materials, including particle packing, segregation and pressure distribution [1–8]. The practice of storing granular materials in the form of sand piles occurs in many industrial situations dealing with particulate materials. Examples include the pharmaceutical industry relying on the processing of powders and tablets, the agricultural industry, coal industry and the food processing industries where seeds, coal (grain) and foods are transported and manipulated. Moreover, the storing of the material in a pile may be useful in fertilizer and mining industries. Thus, the flow of granular materials through a funnel (to form a pile) is an important problem for many industrial processes. In order to handle the processing of granular materials in a pile properly, it is important to understand its mechanical properties. On the other hand, the study of deformation of granular materials either under external loading or unloading is also of practical importance for many industries. Although some progress has been made in this field during last ten years, these properties are still far from being exhaustively understood. Moreover, continuum models proposing constitutive Powder Technology 204 (2010) 113–123 ⁎ Corresponding author. Tel.: + 49 17620961836; fax: + 49203 3792689 E-mail address: pradip.roul@uni-due.de (P. Roul). 0032-5910/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.07.026 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec