Latest news!

News! our OpenFDEM website is online.

08 August 2023

OpenFDEM website is online to public under the contribution by Dr. Xiaofeng Li, Katia (Ekaterina) Ossetchkina and Yuqi (Grace) Hu. The future news about OpenFDEM will be hosted on this webiste and the users can also download the software from this address. Try it at here.

Greetings! Xiaofeng was invited as the scientific editor of Journal of Rock Mechanics and Geotechnical Engineering.

08 October 2022

JRMGE (newest impact factor = 7.3) aims to publish the latest research achievements in rock mechanics and geotechnical engineering. All articles published open access will be immediately and permanently free for everyone to read, download, copy and distribute. see more at here.

Congrats! Xiaofeng was selected as the Future Leader in class 2022 by ARMA.

15 June 2022

The ARMA awards no more than 15 people from all countries every year to support the young outstanding reserachers in the area of geomechanics, rock mechanics, petrolem and mining.

Our new review paper of fracturing behaviour in pre-cracked rocks is online.

20 May 2022

This review outlines the brittle deformation and fracturing properties of pre-cracked rocks. The main experimental techniques used to study the crack stress in rocks are illustrated and the mechanical characteristics regarding crack initiation, propagation and coalescence are discussed. see more at here.

We have a new review paper on dynamic crack propagation been published.

15 March 2022

Understanding the effect of natural imperfects within brittle materials for dynamic problems is crucial in rock mechanics. Typical fracture patterns in terms of the interaction between a propagating crack and a pre-existing weak interface are discussed and the intrinsic mechanism is uncovered in terms of crack deflection criterion. Please find more on Engineering Fracture Mechanics .

Xiaofeng was awarded as 2022 ROCHA runner-up by ISRM.

17 November 2021

The ROCHA medal award committee awarded as the 2022 runner-up, he is the second ROCHA medal receiver nominated by China group. You can find the abstract at here .

New blast module is available in OpenFDEM now.

12 October 2021

The new developed blast module is capable of reproducing the gas penetration process during detonation of explosives, the compressibility of gas flow is also totally considered.

Low resolution of DIC in dynamic test are overcomed by deeplearning hDIC!

26 September 2021

This project aims to solve the dependency on resolution of DIC in high speed test.

Xiaofeng joined in UofT as a Postdoc.

15 September 2021

The new project in UofT will develop a Open source FDEM.


Projects Working On

Research Interests

    My research interests lie in the fields of rock dynamics and computational mechanic sciences with emphasis on hybrid continuum and discontinuum methods development for failure modelling of geomaterials spanning the scale from micro grain-based heterogeneity (mineral, texture, anisotropy, grain morphology) to macro in-situ applications (rock faulting, geothermal-induced earthquakes). Recent researches have included: (a)rock pulverization due to fast earthquakes, insights from the dynamic fragmentation and super-shear faulting, (b)rock-fluid interaction affects the rock deformation and fault activation, (c)the micro behavior of rock minerals in association with nanoindetation, and (d)open-source project of hybrid continuum and discontinuum computational modelling.

    • Open-source code projects: OpenFDEM (binary code coming soon, trial of source code is accessible on request, contact the developer - Dr. Xiaofeng Li)
    • High speed measurements technology and deep learning DIC: deeplearning_hDIC (source code can be shared on request)
    • Multiscale fracturing modelling of heterogeneous materials
    • Micro mechanics of rock materials due to dynamic nanoindetation
    • Fast earthquake induced rock pulverization: insights from micro defects and super-shear faulting

OpenFDEM New Features

    OpenFDEM ( is an open-source(free) and object-oriented finite and discrete element solver for solving diverse multiscale, multiphase and multiphysics (3M) problems accurately with high performance computations. Its applications include but are not limited to mechanical, thermal and fluid dynamics. OpenFDEM also provides a wide range of flexibility in geometry, mesh and material modules.OpenFDEM is constructed by C++, and can be operated with an extensive Python C++ interface.

    OpenFDEM is open-free (first stage) or open-source (second stage) under GNU license and can be used even in comercial softwares as it is before properly get the copyright from the developer.

    This project started from 2018 when I was a PhD candidate in Monash University, and the very basic version was finished in 2020 when I graduated from Institute of Rock and Soil Mechanics. After that, I turned to a full-time developer and PI of this project in University of Toronto since September in 2021. The global FDEM workshop "FDEM-2022 – Modeling innovations and numerical experiments in geomechanics", was held in Toronto on December 9, 2022. The record can be found @ To far, the main new features of OpenFDEM are:

    Timeline of the OpenFDEM project.

    Object Oriented Architecture (C++ and Cuda)

    Modular & Extensible FEM Kernel and DEM Kernel (OpenFDEMlib)

    • Fully extendable and portable - The kernel can be extended in any “direction”. Adding new element types, new materials with any element types and internal history parameters, new boundary conditions (time-dependent, position-dependent, state-dependent, periodic and flow-in/out) or numerical algorithms (explicit and implicit) is possible, as well as the ability to add and manage arbitrary degrees of freedom is a matter of course. (OpenFDEM is intended to be a more general FEM/DEM solver compatible with arbitrary scenarios.) Like other general open-source FEM solvers, the most important feature of OpenFDEM is its standardization and generality, which allows the continuum-discontinuum method to be used with more general scenarios. The limitation of this project is the developers’ thoughts, rather than the method itself.

    • OpenFDEM supports 26 element types and 24 materials.

    • Highly accurate and reliable - The kernel provides high-order integration schemes and solving methods to seek more reliable numerical results which are comparable to theoretical solutions. The element type has a maximum order of three to accurately reproduce the large deformation behavior whithin the entity, and the new kinematic scheme to construct a nonlinear deformation. The Hilber-Hughes-Taylor (HHT) time integration scheme (second-order accuracy) is used for the explicit solver.

    • OpenFDEM feature.

    • Friendly preprocessing interface - The Gmsh is provided to easily create meshes from CAD, geometry file and third-party commercial software. The built-in commands are accessible to crate many basic geometries (e.g. rectangular, circle, ellipse, polygon, line and particles) and initial discontinuities (e.g. single joint, joint sets, DFNs and DFNs from image mapping). The built-in mesh module is able to quickly assess mesh quality and the local bad meshes will be further optimized by swap, node insertion, node delete, element split techniques, automatically or manually.

    • Parallel processing support - Most modules can be operated in parallel and very good performance scalability can be obtained on various platforms. The NBS contact method is not continued in OpenFDEM anymore and a new cell-based contact searching algorithm, having a complexity of O(NlogN) as well is proposed to make the contact searching process is parallelable. Built-in high-level support for dynamic load balancing. The GPU acceleration will be also open shortly.

    • Mesh adaptive analysis support - Local adaptive mesh refinement (lAMR) and global adaptive mesh refinement(gAMR) are provided for mesh optimization and accuracy enhancement. It supports for various error estimations based on different remeshing criteria, support for primary unknown and internal variables mapping, support for high-accuracy internal variable interpolation and fast unbalance equilibrium after refinement. The AMR supports fracture path consistent before and after remeshing.

    • Global adaptive mesh refinement (up-left) and local adaptive mesh refinment (down-right) in OpenFDEM.

      Flowing mesh refined based on the stress level in the bar.

    • Rich grain-based modelling support - Voronoi tessellations can be created with the built-in Voronoi module. The optimization is deployed to match the laboratorial mineral distribution from measurements or digital image. The realistic GBM can be reproduced directly in the project by inputting the binary sample images, the polygonal element type is available for representing the whole mineral individually, further transgranular fracturing can be realized by element splitting techniques.

    • OpenFDEM implements a Voronoi lib and is able to simulate grains directly based on polygonal elements.

    • Large material library - currently, OpenFDEM supports 17 element materials (including elastic, hyperelastic, plastic, damage, nonlocal, viscous and phas—field models), 7 cohesive materials (spanning static, dynamic and fatigue problems), and 6 contact models (including Mohr-coulomb friction, hertz contact, rate friction, rough dilation shear law and so on).

    • New material library in OpenFDEM.

      Phasefield module in OpenFDEM.

    • Advanced analysis solvers - Linear dynamic solver (implicit and explicit), linear static solver (PETSC), eigenvalue problem (SLEPc), and nonlinear dynamic solver (explicit) are applicable for different problems, the implicit solver currently can be run on Linux-like OS.

    Particle Discrete Element Method (pDEM)

    • Rigid DEM support - built-in module for rigid particles packing, kinematics and collision, the particle-based contact models include linear, Hertz, cohesive bond and rotation resistance model.

    • Sand compression test with membrane (left) and irregular deformable and breakable particles packing (right).

    • Realistic Particle Modelling - Overlapping particles and Fourier-Voronoi-based algorithm are used to generate realistic particles having complex shapes. The realistic particles can be rigid or deformable, the breakage of the particles are also possible.

    • Debris flow of rigid particles due to gravity (left) and debris flow of irregular deformable fragments due to gravity (right, stl file from itasca).

    Fluid Dynamic Module

    • Analysis Procedures: matrix flow for pore seepage, transient incompressible fracture flow, transient compressible fracture flow and gas flow problems.

    • Blast considering gas expansion, gas flow by hydro module (left) and without gas expansion by mechanical module (right).

    • Element Library: triangle, quadratic triangle, quadrilateral and quadratic quadrilateral element types are supported for Newtonian fluid and Bingham fluid.

    • Fluid injection in fractured rock block (left), Water flowing in a tube using CFD in hydro module (right).

    • Boundary Types: water level, porepressure, flow rate, steady flow and impermeable boundary conditions are supported in hydro module.

    Thermal transportation module

    • Analysis procedures: matrix thermal transportation, thermal resistance in fractures, heat conduction of fluid in fracture, heat advection of fluid, heat exchange between solid and fluid and contact thermal problems.

      Gabbro fracturing after microwave treatment in thermal module.

    • Element Library: triangle, quadratic triangle, quadrilateral and quadratic quadrilateral element types are supported.

    • Boundary Types: constant temperature, flux, conduction, advection, radiation, source and adiabatic thermal conditions are supported.

    Computational fluid dynamics

    • Material Point Method (MPM) is used to simulate the fluid transportation and large deformation. This mesh-free method does not encounter the drawbacks of mesh-based methods (high deformation tangling, advection errors etc.) which makes it a promising and powerful tool for large deformation problems. The coupling among FDEM and MPM makes the solid interacting with fluid is possible.

      Tapewater flow into a tank, MPM + FDEM.

      Kármán vortex street example, periodic boundary.


    • Export to VTK format is supported, allowing to use VTK based visualization tools (such as ParaView) for postprocessing on different platforms

    • Export to Tecplot format is supported

    • Export historic variables which are monitored at each step to csv is supported.

    Third-Party Packages in OpenFDEM:

    • GMSH - 2D and 3D mesh generator

    • GSL - mathematical routines

    • Eigen- matrix calculator

    • PETSC - Portable, Extensible Toolkit for Scientific Computation

    • ParaView - Parallel Visualization Application (for .vtk files)

Call for papers

special_issue png

    We would like to invite you to submit a contribution to a featured journal issue on FDEM that will be published on J. Rock Mech. Geotech. (Impact Factor = 7.3, ranking 2/41 in Engineering and geological) in 2024.

    The combined hybrid finite-discrete element method (FDEM) is widely used for modeling fracturing and fragmentation processes in brittle materials such as rock and concrete. The intrinsic advantage of FDEM derives by its ability to combine continuum mechanics formulations, such as finite strain-based deformability and non-linear fracture mechanics, with discrete element method, allowing the seamless transition from a continuum to a discontinuum model. FDEM allows to model multiple crack initiation, propagation and nucleation at micro scale to fractures or fragments at macro scale. These advances promote the applications of FDEM in geomechanics, energy storage, geothermal energy extraction, rock engineering, oil and gas exploration and mining. In recent decades, the FDEM has matured into a more general-purpose numerical method, covering mechanical, hydraulic, thermal and chemical coupling, that can be used to tackle increasingly more complex multiphase, multiphysics and multiscale problems.

    This Special Issue aims to highlight the new advances and future developments of combined finite-discrete element method or continuum-discontinuum method, for fracturing and fragmentation in geomechanics, underground energy storage, nuclear waste disposal, enhanced geothermal system, civil engineering or mining. All the papers on this special issue will be open access and free.

    The main topic includes but not limited to:

    • Multiscale, multiphase, and multiphysics modeling of fracture and fragmentation in rock mechanics and rock engineering

    • New advances and future developments of combined finite-discrete element method

    • High-Performance computing application and large-scale modelling in combined finite-discrete element method

    • Novel contact algorithms for high efficiency and accuracy

    • Hydraulic fracturing and fluid transportation modelling in energy storage or fractured reservoirs

    • THM(C) coupling in enhanced geothermal systems (EGS), underground hydrogen storage (UHS), nuclear waste disposal and CO2 storage

    • Computational fluid dynamics and fluid-solid interaction for rock fracturing modelling

    • Artificial intelligence and machine learning technique in combined finite-discrete element method

    You are invited to submit your manuscript at any time before the submission deadline. For any inquiries about the appropriateness of contribution topics, please contact Dr. Xiaofeng Li via

    Guest Editors

    Dr. Giovanni Grasselli
    Department of Civil & Mineral Engineering
    University of Toronto, Toronto, CA, Canada

    Dr. Haibo Li
    Institute of Rock and Soil Mechanics
    Chinese Academy of Sciences, Wuhan, China

    Dr. Xiaofeng Li
    Department of Civil & Mineral Engineering
    University of Toronto, Toronto, CA, Canada