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This paper discusses the issues involved in the development of combined finite/discrete element methods; both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems. The finite element representation of the solid region is combined with progressive fracturing, which leads to the formation of discrete elements, which may be composed of one or more deformable finite elements. The applicability of the approach is demonstrated by the solution of a range of examples relevant to various industrial sections.

The purpose of this paper is to present a new numerical model based on a combined finite-discrete element method, capable of predicting the behaviour of reinforced concrete structures under dynamic load up to failure.

An embedded model of reinforcing bars is implemented in combined finite-discrete element code. Cracking of the structure was enabled by a combined single and smeared crack model. The model for reinforcing bars was based on an approximation of the experimental curves for the bar strain in the crack. The developed numerical model includes interaction effects between reinforcement and concrete and cyclic behaviour of concrete and steel during dynamic loading.

The findings provide a realistic description of cracking in the concrete structure, where all non-linear effects are realized in joint elements of the concrete and reinforcing bars. This leads to a robust and precise model for non-linear analysis of reinforced concrete structures under dynamic load.

This paper presents new robust finite-discrete element numerical model for analysis and prediction of the collapse of reinforced concrete structures. The model is capable of including the effects of dynamic loading on the structures, both in the linear-elastic range, as well as in the non-linear range including crack initiation and propagation, energy dissipation due to non-linear effects, inertial effects due to motion, contact impact, and the state of rest, which is a consequence of energy dissipation in the system.

This paper outlines a dynamic domain decomposition‐based parallel strategy for combined finite/discrete element analysis of multi‐fracturing solids and discrete systems. Attention is focused on the parallelised interaction detection between discrete objects. Two graph representation models for discrete objects in contact are proposed which lay the foundation of the current development. In addition, a load imbalance detection and re‐balancing scheme is also suggested to enhance the parallel performance. Finally, numerical examples are provided to illustrate the parallel performance achieved with the current implementation.

Continua and discontinua coexist in natural rock materials. This paper aims to present an improved approach for addressing the mechanical response of rock masses based on the combined finite-discrete element method (FDEM) proposed by Munjiza.

Several algorithms have been programmed in the new approach. The algorithms include (1) a simpler and more efficient algorithm to calculate the contact force; (2) An algorithm for tangential contact force closer to the actual physical process; (3) a plastic yielding criterion (e.g. Mohr-Coulomb) to modify the elastic stress for fitting the mechanical behavior of elastoplastic materials; and (4) a complete code for the mechanical calculation to be implemented in Matrix Laboratory (MATLAB).

Three case studies, including two standard laboratory experiments (uniaxial compression and Brazilian split test) and one engineering-scale anti-dip slop model, are presented to illustrate the feasibility of the Y-Mat code and its ability to deal with multi-scale rock mechanics problems. The results, including the progressive failure process, failure mode and trajectory of each case, are acceptable compared to other corresponding studies. It is shown that, the code is capable of modeling geotechnical and geological engineering problems.

This article gives an improved FDEM-based numerical calculation code. And, feasibility of the code is verified through three cases. It can effectively solve the geotechnical and geological engineering problems.

In order to avoid the problem of volumetric locking often encountered when using constant strain tetrahedral finite elements, the purpose of this paper is to present a new composite tetrahedron element which is especially designed for the combined finite-discrete element method (FDEM).

A ten-noded composite tetrahedral (COMPTet) finite element, composed of eight four-noded low order tetrahedrons, has been implemented based on Munjiza’s multiplicative decomposition approach. This approach naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. The problem of volumetric locking is avoided via a selective integration approach that allows for different constitutive components to be evaluated at different integration points.

A number of validation cases considering different loading and boundary conditions and different materials for the proposed element are presented. A practical application of the use of the COMPTet finite element is presented by quantitative comparison of numerical model results against simple theoretical estimates and results from acrylic fracturing experiments. All of these examples clearly show the capability of the composite element in eliminating volumetric locking.

For this tetrahedral element, the combination of “composite” and “low order sub-element” properties are good choices for FDEM dynamic fracture propagation simulations: in order to eliminate the volumetric locking, only the information from the sub-elements of the composite element are needed which is especially convenient for cases where re-meshing is necessary, and the low order sub-elements will enable robust contact interaction algorithms, which maintains both relatively high computational efficiency and accuracy.

The purpose of this paper is to present a 2D combined finite‐discrete element method (FEM‐DEM) to model the multi‐fracture of beam structures and an application of the method to an ice‐structure interaction problem.

In the method, elastic beams and their fracture are modelled according to FEM by using nonlinear Timoshenko beam elements and cohesive crack model. Additionally, the beam elements are used to tie the discrete elements together. The contact forces between the colliding beams are calculated by using the DEM.

Three numerical examples are given to verify the method. Further, the method is applied to model the failure process of a floating ice beam against an inclined structure. Based on the comparison of the experiments and the simulation, a good agreement between the results is observed.

In the context of combined FEM‐DEM, the two novel features presented in this paper are: the use of Timoshenko finite element beams with damping to calculate internal forces and to combine the discrete elements; and the bending failure by the cohesive crack approach while simultaneously keeping track of the position of the neutral axis of the beam.

This paper aims to present a new numerical model for geometric nonlinear analysis of thin-shell structures based on a combined finite-discrete element method (FDEM).

The model uses rotation-free, three-node triangular finite elements with exact formulation for large rotations, large displacements in conjunction with small strains.

The presented numerical results related to behaviour of arbitrary shaped thin shell structures under large rotations and large displacement are in a good agreement with reference solutions.

This paper presents new computationally efficient numerical model for geometric nonlinear analysis and prediction of the behaviour of thin-shell structures based on combined FDEM. The model is implemented into the open source FDEM package “Yfdem”, and is tested on simple benchmark problems.

Some issues related to effective parallel implementation of the combined finite‐discrete element approach on PC clusters are discussed. Attention is focused on the interprocessor communications. Three communication schemes suitable for different problems are presented. The worker‐to‐manager scheme is simple to implement. The neighbour‐to‐neighbour scheme is sophisticated with regard to programming, and requires extra memory space, but has good overall performance for larger problems. The mixed worker‐manager scheme can balance the difficulty in programming and the overall communication performance. The effects of subdomain buffer zone on communications are also demonstrated by numerical examples.

This paper aims to investigate the responses of laminated glass under soft body impact, including elastic impact and fracture/fragmentation consideration.

The simulation uses the combined finite-discrete element method (FDEM) which combines finite element mesh into discrete elements, enabling the accurate prediction of contact force and deformation. Material rupture is modelled with a cohesive fracture criterion, evaluating the process from continua to discontinua.

Responses of laminated glass under soft impact (both elastic and fracture) agree well with known data. Crack initiation time in laminated glass increases with the increase of the outside glass thickness. With the increase of Eprojectile, failure mode is changing from flexural to shear, and damage tends to propagate longitudinally when the contact surface increases. Results show that the FDEM is capable of modelling soft impact behaviour of laminated glass successfully.

The work is done in 2D, and it will not represent fully the 3D mechanisms.

Elastic and fracture behaviour of laminated glass under soft impact is simulated using the 2D FDEM. Limited work has been done on soft impact of laminated glass with FDEM, and special research endeavours are warranted. Benchmark examples and discussions are provided for future research.

The purpose of this paper is to propose a novel combined finite-discrete element method (FDEM), based on the cohesive zone model, for simulating rockslide problems at the laboratory scale.

The combined FDEM is realized using ABAQUS/Explicit. The rock mass is represented as a collection of elastic bulk elements glued by cohesive elements with zero thickness. To reproduce the tensile and shear micro-fractures in rock material, the Mohr-Coulomb model with tension cut-off is employed as the damage initiation criterion of cohesive elements. Three simulated laboratory tests are considered to verify the capability of combined FDEM in reproducing the mechanical behavior of rock masses. Three slope models with different joint inclinations are taken to illustrate the application of the combined FDEM to rockslide simulation.

The results show that the joint inclination is an important factor for inducing the progressive failure behavior. With a low joint inclination, the slope failure process is observed to be a collapse mode. As the joint inclination becomes higher, the failure mode changes to sliding and the steady time of rock blocks is shortened. Moreover, the runout distance and post-failure slope angle decrease as the joint inclination increases.

These studies indicate that the combined FDEM performed within ABAQUS can simulate slope stability problems for research purposes and is useful for studying the slope failure mechanism comprehensively.