A numerical investigation of mesh sensitivity for a newthree-dimensional fracture model within the combinedfinite-discrete element methodLiwei Guoa, Jiansheng Xianga, John-Paul Lathama, Bassam IzzuddinbaDepartment of Earth Science and Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United KingdombDepartment of Civil and Environmental Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdoma r t i c l ei n f oArticle history:Received 24 August 2015Received in revised form 11 November 2015Accepted 14 November 2015Available online 22 November 2015Keywords:Numerical investigationThree-dimensional fracture modelMesh size sensitivityMesh orientation sensitivityCombined finite-discrete element methoda b s t r a c tRecently a new three-dimensional fracture model has been developed in the context of thecombined finite-discrete element method. In order to provide quantitative guidance forengineering applications, mesh size and orientation sensitivity are investigated by spe-cially designed numerical tests. The mesh size sensitivity is analysed by modelling a singletensile fracture propagation problem and three-point bending tests using a series of mod-els with the same geometry but different structured mesh sizes. The mesh orientation sen-sitivity is investigated by diametrically compressing a disc specimen of unstructuredmeshes from different angles. The computational efficiency of the three-dimensional frac-ture model is also studied.? 2015 The Authors. Published by Elsevier Ltd. ThisisanopenaccessarticleundertheCCBYlicense (http:/creativecommons.org/licenses/by/4.0/).1. IntroductionIn the field of numerical modelling of fractures in quasi-brittle materials, linear and non-linear elastic fracture mechanicsbased methods 13, the extended finite element method (XFEM) 46 and meshless methods, such as the element freeGalerkin method (EFGM) 7,8 have traditionally been in the dominant positions. Due to the discrete nature of fractureand fragmentation behaviour, discontinuum-based numerical methods that are originally used for granular materials, suchas the smoothed particle hydrodynamics (SPH) method 911 and the discrete element method (DEM) 1214 have alsobecome increasingly popular. In actual numerical simulations of engineering applications, the choice of modelling approachshould be based on the likely failure mechanism of the material, i.e. whether it is a failure of material, discontinuity or a com-bination of both 15.To fully explore and extend the potential of different numerical methods, there is an increasing interest in combiningFEM-based and DEM-based methods to converge to a formulation that has the advantage of using the DEM to capturethe discrete behaviour during fracture and fragmentation processes while retaining the accurate characterisation of defor-mation and stress fields using the FEM. It should be noted that the literature mentioned in this section is not meant to be acomprehensive review of numerical methods in fracture modelling, but a tailored one with the focus on using combined FEMand DEM formulations. In this category, different research groups have come up with various strategies in the developmenthttp:/dx.doi.org/10.1016/j.engfracmech.2015.11.0060013-7944/? 2015 The Authors. Published by Elsevier Ltd.This is an open access article under the CC BY license (http:/creativecommons.org/licenses/by/4.0/).Corresponding author at: Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom.Tel.: +44 (0)20 3108 9514.E-mail addresses: liwei.guoucl.ac.uk (L. Guo), j.xiangimperial.ac.uk (J. Xiang), j.p.lathamimperial.ac.uk (J.-P. Latham), b.izzuddinimperial.ac.uk(B. Izzuddin).Engineering Fracture Mechanics 151 (2016) 7091Contents lists available at ScienceDirectEngineering Fracture Mechanicsjournal homepage: formulations and numerical implementations. For example, Monteiro Azevedo and Lemos 16 proposed a hybrid DEMand FEM method that uses the DEM in the discretisation of the fracture zone and the FEM for the surrounding area so frac-tures can propagate along particle boundaries in DEM discretised zones. Morris et al. 17 discretised the discrete blocksinternally with tetrahedral elements, and implemented Cosserat point theory and cohesive element formulations to simulatefractures. Paavilainen et al. 18 presented a two-dimensional combined FEM and DEM method, which uses the nonlinearTimoshenko beam element and the cohesive crack model for the FEM part. The contact forces between colliding beamsare calculated by the DEM part. Kh. et al. 19 developed a two-dimensional combined DEM and FEM model to simulatebreakage of angular particles in granular systems. In their model, all particles are simulated by the DEM, and after each stepof DEM analysis every particle is individually modelled by the FEM to determine if it will break. Lei et al. 20 and Rougieret al. 21 developed a three-dimensional