Abstract—The hybrid finite-discrete element method (FDEM) has become a highly popular means of simulating the failure process in natural and engineered materials due to its ability to model the transition from continuum to discontinuum by means of fracture and fragmentation processes. In this article the progress and status of FDEM application in research is reviewed systematically from the following four aspects: the fundamentals of theory and methodology, fracture and contact models, graphical user interface, and applications. In addition, the authors point out the primary research directions in which FDEM is being applied to good effect. Index Terms—Finite element method, Discrete element method, Finite-discrete element method I. INTRODUCTION NGINEERING materials are usually considered to form a continuum when modeling their mechanical behavior. This convention arises from the earliest needs of engineering design for load bearing applications, from civil construction to machine components. Therefore, the continuum methods are most c ommonly used, including th e boundary-element methods (BEM), the finite element methods (FEM), and the finite-difference methods (FDM). However, e xplicit representation o f the o nset a nd d evelopment o f f racture, crack propagation under monotonic and cyclic loading, and the p rogression t owards c atastrophic f ailure ar e v ery important aspects of modern engineering design, particularly in vi ew of the importance of s uch a pproaches as damage-tolerant design that has found widespread use in the aerospace i ndustry. I ncorporating f racture i n t he cl assical continuum numerical methods is not straightforward, mainly because o f the scale d ifference b etween o bject s ize an d fracture features, and the continuum a ssumptions that lie a t the very core of the computational structure. The limitations of c ontinuum methods motivated th e development of the discrete element methods (DEMs) [1-8]. By combining D EM w ith F EM, through each d iscrete Manuscript received April 2nd, 2016; revised April 20, 2016. This work was partially supported by EU FP7 project iSTRESS (604646) as well as by EPSRC via grants EP/I020691, EP/G004676 and EP/H003215. Guanhua Sun is an associate professor in the Institute of Rock and Soil Mechanics, t he C hinese A cademy o f Sciences, Mid. 1 2, Xiaohongshan, Wuchang, Wuhan, 430071, P. R. China, and now is academic visitor at the Department o f E ngineering S cience, University o f O xford, O X1 3 PJ, U K (e-mail: ghsun@whrsm.ac.cn). Tan Sui i s a postdoctoral r esearcher i n the D epartment o f E ngineering Science, University o f O xford, O X1 3PJ, U K (e -mail: tan.sui@eng.ox.ac.uk). *Alexander M . K orsunsky i s a p rofessor o f t he D epartment o f Engineering Science a t t he U niversity o f O xford, O X1 3PJ, U K (corresponding a uthor, tel: + 44-18652-73043; f ax: + 44-18652-73010; e-mail: alexander.korsunsky@eng.ox.ac.uk). element being sub-divided into finite elements, the combined finite-discrete el ement method ( FDEM) was proposed by Munjiza [9-10]. The advantage of this approach lies in the fact t hat deformability can b e w ell represented by f inite elements, whilst d iscontinuities such a s cracks c an b e explicitly described by discrete elements. Thus FDEM can be used to simulate th e both continuous a nd di scontinuous mechanical behavior, and capture the entire loading a nd crack path and the gradual degradation process of materials that undergo progressive fracture. The distinguishing feature of F DEM i s its ability to simulate the transition from continuum to discontinuum that is the most crucial aspect of the fracture and fragmentation processes [11]. The key aspects of the analysis procedure in FDEM i nclude contact d etection, p recise d escription o f t he interaction and f riction between d iscrete e lements, el astic deformation of the finite e lements, and crack creation a nd propagation within and between finite elements. The past decades have w itnessed many developments in the following aspects of FDEM: the fundamental theory and method; fracture and contact mechanics modelling; graphical user interface development and flexibility; and demonstration of the method’s power for specific applications. In this article these as pects o f r esearch p rogress are r eviewed, and the outlook is summarized. II. PROGRESSES IN FDEM A. Fundamental Theory and Method In t he p ast decades important progress has b een made in the fundamental theory and methodology. Firstly, a most significant facet of FDEM capability is an excellent c ontact d etection a lgorithm that a llows e fficient identification of all pairs of nodes in contact, and, conversely, the removal from the list of contacting pairs of those couples of n odes that p reviously were co nsidered t o b e in close contact, but have moved sufficiently far apart to be removed from the list. In the original FDEM code, the so-called “No Binary S earch” ( NBS) contact d etection a lgorithm [9, 1 2] was i mplemented (Munjiza, [ 9-10]). T he NBS a lgorithm remains t he most e fficient and hi ghly developed contact detection a lgorithms till now, s ince unlike a ny a lgorithm based on binary for which the total CPU time for detecting all contacting co uples s cales as N lnN with the number of discrete e ntities N, t he Munjiza-NBS algorithm is a linear function ~N of the total number of discrete elements. In the following years, many researchers focused their efforts on the development of th is b asic id ea based on the o riginal co des. For ex ample, a prescriptive p rocedure t o ar rive at a combination o f in put p arameters for t he n ewly de veloped Y-Geo FDEM code was developed designed to be used in Review of the Hybrid Finite-Discrete Element Method (FDEM) Guanhua Sun, Tan Sui, Alexander M. Korsunsky* E Proceedings of the World Congress on Engineering 2016 Vol II WCE 2016, June 29 - July 1, 2016, London, U.K. ISBN: 978-988-14048-0-0 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2016