Discrete Finite Element Model Research Articles

Advanced tensile fracture analysis of alumina ceramics: Integrating hybrid finite-discrete element modeling with experimental insights

This study offers novel insights into the Mode I tensile response of an alumina ceramic through the use of computational modeling and the flattened Brazilian disk (FBD) experiments. A modified hybrid finite-discrete element method (HFDEM) is developed, integrating a coupled damage and friction cohesive model and a microscopic stochastic fracture model with a Weibull strength distribution by Monte Carlo simulation. The model is used to simulate direct tensile failure processes under quasi-static loading conditions, providing qualitative and quantitative predictions of direct tensile failure processes of an alumina ceramic. Concurrently, quasi-static flattened Brazilian disk tests (indirect tensile tests) are performed on a standard MTS machine coupled with a high-speed camera. The modified HFDEM model is also applied to reproduce the FBD experiments, and our simulated tensile strength is consistent with the experimental results. The results of the modified HFDEM model show three kinds of phenomena (i.e., “underestimation”, “reasonable estimation”, and “overestimation” of the indirect tensile strength) and four different types of associated fracture and fragment patterns of FBD testing. The integration of simulation and experimental results reveal relationships between fracture patterns, fragment geometry, tensile strength, and indirect tensile strength. The fracture and fragmentation patterns derived from our modified HFDEM model can be utilized to analyze the “tensile strength” measured in BD testing. Overall, this research offers important insights and direction for future Brazilian disk experiments and tensile strength assessments, enhancing our comprehension of ceramic failure mechanisms under tensile loadings.

Propagation and complex morphology of hydraulic fractures in lamellar shales based on finite-discrete element modeling

We explore the controls of stress magnitude and orientation relative to bedding on the resulting morphology/topology of hydraulic fractures using a combined finite-discrete element method (FDEM). Behavior is shown conditioned by the ratio of principal stresses λ=σ3/σ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda ={\\sigma }_{3}/{\\sigma }_{1}$$\\end{document} and relative inclination of the bedding. When the lateral pressure coefficient (λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}) is less than 0.67, hydraulic fractures predominantly initiate as tensile fractures along the wellbore, aligning with the maximum principal stress direction. Conversely, for λ≥0.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda \\ge 0.67$$\\end{document}, shear cracks are favored to initiate for the minor stress difference, leading to a less predictable initiation and extension direction. Simultaneously, diminished stress differences correspond to elevated reservoir breakdown pressures, displaying a linear correlation with lateral pressure coefficients and little influenced by equivalent bedding orientation. Bedding plane orientation significantly impacts the mode and morphology of hydraulic fracture propagation. Bedding parallel to the direction of the minimum principal stress (σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{3}$$\\end{document}) favors layer-penetrating and bifurcated fractures, whereas inclined bedding facilitates the emergence of numerous steering-type and capture-type fractures. Especially at steeper inclinations (β=60∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta =60^\\circ$$\\end{document}), hydraulic fractures readily extend along the bedding surface, inducing macroscopic shear slip failure. Under high-stress disparities, the breakdown pressure exhibits greater sensitivity to bedding inclination, and its influence pattern aligns with the variations in tensile strength, typically reaching maximum and minimum values at bedding inclination angles of 0° and 60°, respectively.

Combined Finite-Discrete Element Model Simulations of Shake-Table Tests on a Full-Scale Masonry Cross Vault

ABSTRACT This work presents the numerical simulations of shaking table tests of a full-scale masonry cross vault. The boundary conditions simulate the presence of a continuous lateral wall and of a colonnade-between-naves condition. The seismic action is applied along the longitudinal direction of the specimen, with increasing amplitude. The model used for the simulations allows for the elastic finite element modelling of masonry units and the discrete element modelling of the interfaces between them. A tension cut-off governs the interface: no tensile stress can be transmitted once this strength is exceeded. The shear response is defined by cohesion and friction: once the former is exceeded the interface reacts according to Coulomb’s behaviour. The simulations are related to the blind predictions, according to the scheduled tests, and the post-dictions, according to the actual testing sequence. The prediction model overestimates displacements and does not catch the actual crack distribution. Therefore, a post-simulation model was implemented, revising the masonry elastic modulus as well as the stiffness and boundary conditions of the supporting piers. Simulations are improved both in terms of displacement predictions and damage mechanism. Finally, the sensitivity to finite-element size, damping ratio and block discretisation was explored.

Study on the interaction between hydraulic fracture and natural fracture under high stress

The existence of natural fractures in the reservoir has a great influence on the formation of complex fracture network, but the interaction between hydraulic fractures and natural fractures under high stress was rarely studied. Through laboratory tests, the law and characteristics of the interaction between hydraulic fractures and natural fractures under high stress were studied from the aspects of natural fractures angle, size, quantity, production method and ground stress in this study. Based on these interaction characteristics, a complex fracture network formation method of deep reservoir was proposed, which provided reference for engineering practice. The criterion of interaction between hydraulic fracture and natural fracture was improved, and the calculation method of rock tensile strength in three-dimensional state was proposed, which was applied to the criterion of fracture opening and fracture expansion. Combined with laboratory tests, a special interaction mode of hydraulic fracture passing through a certain position from the direction to end A (F-Type crossing mode) under high stress was proposed, and the criterion of this interaction mode were obtained. The three-dimensional finite discrete element model (FDEM) was used to investigate the effects of natural fracture strength and fracturing fluid viscosity on hydraulic fracture propagation under high stress. The results showed that the natural crack strength has great influence on the width, volume and shape of hydraulic crack. Small difference of fracturing fluid viscosity has little influence on fracture propagation, but high viscosity fracturing fluid has a greater influence on fracture propagation. This study provided reference for hydraulic fracturing engineering.

A modeling study of elastoplastic rock failure regime based on finite discrete elements

Numerical simulation has become a pivotal method in geotechnical engineering for analyzing rock failure. However, traditional model lacks comprehensive elastoplastic rock characterization. Therefore, a new finite-discrete element model using the Drucker-Prager criterion and cohesive elements based on a traction-separation law to accurately simulate elastoplastic rock breaking has been built. A scratch test simulation is conducted to describe the mechanical response and failure characteristics of the rock during the cutting process. Rock failure characteristics derived from numerical simulations align closely with experimental observations. These simulations successfully replicate both the ductile and brittle regimes observed during scratch tests. Furthermore, they provide insights into the primary driving factors behind rock failure under different regimes. Variation of cutting force and specific energy obtained from the model are entirely consistent with experimental results, with the specific energy decreasing following a −0.5 power law, thus explaining the energy dissipation rule of the specific energy decrease. In brittle regime, crush zones and the resulting rough shearing surface are observed, plastic damage is also found, revealing that the cutter tip is the key structure influencing them. The model established in this paper holds significant importance for rock mechanical property evaluation and the optimization design of cutter structures.

Finite discrete element modeling of desiccation fracturing in partially saturated porous medium

In this study, a numerical framework is presented for the analysis of desiccation fracturing in variably saturated porous media. The solid phase deformation and fracturing are obtained based on the 2D finite-discrete element method (FDEM), while the fluid flow is characterized by nonlinear Richards’ equation and solved by finite volume discretization. The coupling between phases is realized by Biot’s porous media theory. The capabilities of the model in capturing the unsaturated porous medium flow and coupled hydro-mechanical effects are put to the test against benchmark solutions available in the literature. Furthermore, mechanisms of desiccation cracking in the soil are thoroughly investigated through various numerical test cases. In line with experimental observations, results indicate that the type of mechanical constraints and saturation gradients are two main factors contributing to the generation of cracks in desiccation processes.

Combined finite-discrete element modelling of hydraulic fracturing in reservoirs with filled joints

Hydraulic fracturing (HF) is known to be the most effective stimulation to enhance fractured reservoir permeability. The efficiency of an HF fluid injection largely depends on the pre-existing discontinuities or sources of heterogeneities. These features need to be considered in an HF operation design. Amongst these features, rock masses with filled joints are largely ignored despite their presence in deep rocks. This study focuses on HF development in such ground conditions and simulates their hydro-mechanical behavior by using the combined finite-discrete element method (FDEM), which is fully capable of modelling HF propagation in heterogeneous rocks. First, the interaction mechanism between an HF and a closed joint with approaching angles of 30, 60, and 90° is studied. The influences of flow rate, fluid kinematic viscosity, and confining in-situ stresses are evaluated. Then models with a single filled joint with approaching angles of 30, 60, and 90° are studied, interaction types explored, and failure types revealed by varying flow rate, fluid kinematic viscosity, and in-situ stresses. Having explored the interaction mechanism between an HF and a filled joint, three models with complex joint sets are considered; Voronoi filled joint, orthogonal filled joints, and randomly distributed discrete fracture networks (DFNs). The results show a complex interaction mechanism between the HFs and the filled joints. It is revealed that increasing approaching angle, flow rate, or fluid kinematic viscosity causes the development of more shear failure than tensile in models with Voronoi or orthogonal filled joints. However, it is shown that HF's interaction with the DFN is minimal and tensile failure governs considerably.

Combined finite-discrete element modelling of hydraulic fracturing in deep geologically complex reservoirs

Hydraulic fracturing is known to be one of the most effective stimulation techniques to enhance reservoir permeability. A hydraulic fracture (HF) fluid injection's efficiency largely depends on the pre-existing sources of heterogeneities. Amongst these features, conglomerate reservoirs containing blocks in a matrix and rock masses with filled joints are largely ignored despite their presence in deep rocks. This study focuses on the HF development in such reservoir conditions using the combined finite-discrete element method (FDEM). First, the capabilities of the FDEM are verified against available analytical solutions and experimental data. The influence of a single or multiple types of blocks is studied in the conglomerate models. Various controlling parameters including in-situ stresses, flow rate, fluid viscosity, directional HF (DHF), distance between the injection points, properties of the block and matrix interface are considered, and their effects on the hydraulic fracturing path are investigated. In the second scenario, the effect of the joints' filling material is studied, models containing randomly distributed filled joints are built and several controlling factors including different filling materials, angle of approach, in-situ stresses, flow rate and fluid viscosity are considered. The analysis results show a significant influence of both blocks in the matrix and filled joints on the HF pattern. The HF interaction with these features is shown to be complex, and six interaction types for the blocks and nine interaction types for the filled joints are identified based on the close examination of the results.

A combined finite-discrete element model for elasto-capillary phenomena

Elasto-capillary phenomena, involving finite deformation of elastomer and elasto-capillary effect of droplet/film, widely exist in biological and micro-electro-mechanical systems. To quantitatively analyze the influence of surface tension and to accurately predict the deformation of elastomer, we develop a finite strain model of hyperelastic materials, and then solve it by the explicit dynamics employing the combined finite-discrete element method (FDEM). Based on our model, we investigate the expansion of a small cavity in elastomer and examine the relation between radius and pressure of cavity. Besides, we explore the deformation of an elastic rod that is immersed in liquid and subjected to surface tension. Results show that when the elasto-capillary effect is neglected, edges of the rod would be unrealistically roughened, while the surface is actually smoothed as the surface tension increases. Moreover, we explore the elasto-capillary effect on advanced multiple-period wrinkling patterns in both planar and curved film–substrate systems, showing that the rough wavy surface can be smoothed by increasing surface tension. Our results not only provide fundamental insights into a variety of elasto-capillary phenomena, but also offer a platform to quantitatively guide rational designs of flexible smart devices actuated by surface tension.

Investigation on Thermal Buckling of Functionally Gradient Material-Coated Cylindrical Shell Considering Material Properties Varying With Temperature

Abstract Although the thermal buckling problem of functionally gradient material (FGM) cylindrical shells has been investigated for many years, its theoretical solution is rarely reported when considering the material properties varying with temperature, and the existing commercial software also cannot directly solve the critical temperature rise of thermal buckling. Therefore, the theoretical solution of critical temperature rise was first derived for the FGM-coated cylindrical shell with temperature-dependent material properties based on the Donnell thin shell theory. And then, a stepped layer discrete finite element (FE) model was developed by integrating the bisection method into a user subroutine to calculate the critical temperature rise. The results show that the theoretical solutions are in good agreement with the numerical ones, and find out the temperature has a relatively large negative effect on the thermal buckling resistance of the FGM-coated cylindrical shell. Finally, the influence factors on the critical temperature rise were discussed in detail, and some suggestions have been formed to improve the calculation accuracy. This work not only provides a theoretical calculation formula but also develops an FE numerical method to calculate the critical temperature rise of the FGM-coated cylindrical shell, which will help the engineers to design the FGM-related structures easily.

Hybrid Finite-Discrete Element Modeling of the Mode I Tensile Response of an Alumina Ceramic

We have developed a three-dimensional hybrid finite-discrete element model to investigate the mode I tensile opening failure of alumina ceramic. This model implicitly considers the flaw system in the material and explicitly shows the macroscopic failure patterns. A single main crack perpendicular to the loading direction is observed during the tensile loading simulation. Some fragments appear near the crack surfaces due to crack branching. The tensile strength obtained by our model is consistent with the experimental results from the literature. Once validated with the literature, the influences of the distribution of the flaw system on the tensile strength and elastic modulus are explored. The simulation results show that the material with more uniform flaw sizes and fewer big flaws has stronger tensile strength and higher elastic modulus.

Pre- and post-simulations of shake-table tests on a stone masonry building aggregate using finite-discrete elements

AbstractThis work presents the simulations of the non-linear dynamic response of a three-dimensional finite-discrete element model. The model simulates a half-scale masonry building aggregate tested on a shake table by other Authors. The aggregate is made of two un-connected building units having different heights and slightly different wall thicknesses. The floors are made of timber beams and boards. The modelling approach accounts jointly for in-plane and out-of-plane responses, which can be expected given the high flexibility of the floors, and for the separation between the two building units. The simulations are related both to the blind predictions, according to a scheduled testing sequence, and to the post-dictions according to the actual testing sequence and some model calibrations. The prediction model overestimates displacements, underestimates base shear and fairly predicts the damage pattern of comparable experimental runs. The use of the recorded shake table motion improves the accuracy of the post-diction simulations, while still delivering beam unseating. A higher Young’s modulus of the blocks improves markedly the predictions. The strengthening intervention with steel angles connecting floors to walls is only approximately modelled and does not improve the outcomes of the simulations. In summary, the adopted modelling approach is capable of accounting for the pounding between the two building units, predicting the most significant damage as well as estimating approximate average of peak values of base shear and displacements, while individual time histories are less accurately estimated.

A Numerical Study on the Influence of Strain Rate in Finite-Discrete Element Simulation of the Perforation Behaviour of Woven Composites.

Predicting the perforation limit of composite laminates is an important design aspect and is a complex task due to the multi-mode failure mechanism and complex material constitutive behaviour required. This requires high-fidelity numerical models for a better understanding of the physics of the perforation event. This work presents a numerical study on the perforation behaviour of a satin-weave S2-glass/epoxy composite subjected to low-velocity impact. A novel strain-rate-dependent finite-discrete element model (FDEM) is presented and validated by comparison with experimental data for impacts at several energies higher and lower than their perforation limit. The strain rate sensitivity was included in the model by developing a novel user-defined material model, which had a rate-dependent bilinear traction separation cohesive behaviour, implemented using a VUSDFLD subroutine in Abaqus/Explicit. The capability of the model in predicting the perforation limit of the composite was investigated by developing rate-sensitive and insensitive models. The results showed that taking the strain rate into account leads to more accurate predictions of the perforation limit and damage morphology of the laminate subjected to impacts at different energies. The experimental penetration threshold of 89 J was estimated as 79 J by the strain-rate-sensitive models, which was more accurate compared to 52 J predicted by the strain-rate-insensitive model. Additionally, the coupling between interlaminar and intralaminar failure modes in the models led to a more accurate prediction of the delamination area when considering the rate sensitivity.

Numerical investigation of laboratory hydraulic fracturing tests in Pocheon granite

This study investigates numerically several hydraulic fracturing experiments that were performed on intact cubic Pocheon granite samples applying different injection protocols. The goal of the laboratory experiments is to test the concept of cyclic soft stimulation which aims to increase permeability sustainably among others. The Irazu 2D numerical code is used to simulate explicitly coupled hydraulic diffusion and fracturing processes under bi-axial stress conditions. Using the hybrid finite-discrete element modelling approach, we test two injection schemes, constant-rate continuous injection and cyclic progressive injection on homogeneous and heterogeneous samples. Our study focuses on the connection between the geometry of hydraulic fractures, fracturing mechanisms and the permeability increase after injection. The models capture several characteristics of the hydraulic fracturing tests using a time-scaling approach. The numerical simulation results show good agreement with the laboratory experiments in terms of pressure evolution characteristics and fracture pattern. Based on the simulation results, the constant-rate continuous and cyclic progressive injection schemes applied to heterogeneous rock sample with pre-existing fractures show the highest hydraulic aperture increase, and thus permeability enhancement.

Effects of the embedding of cohesive zone model on the mesoscopic fracture behavior of Concrete: A case study of uniaxial tension and compression tests

The application of the Cohesive Zone Model (CZM) in concrete meso-mechanics solves the nonlinear problem of material crack tip well. At present, the application methods of CZM in concrete mesoscopic models include the bond mechanics characterization of the aggregate-mortar interface transition zone (ITZ) and the characterization of fracture characteristics between material micro-elements. From this, two different numerical models were derived—the combined Finite Discrete Element (FDEM) model and the Cohesive Finite Element (CFEM) model. To evaluate the difference between the two numerical models and the traditional Finite Element (FEM) model in simulating concrete mechanical behavior and crack propagation, a 3D concrete mesostructure modeling algorithm was developed in this study, including innovations in gravitational self-compacting of polyhedral aggregates. After that, the FDEM model and the CFEM model were successfully constructed based on the FEM model. Through uniaxial compression and tensile numerical simulations, it was found that the CFEM model is more in line with the theoretical and experimental mechanisms in the characterization of the static mechanical behavior and fracture process of concrete. The fracture failure angle variable defined by the CFEM model revealed that the compressed concrete material exhibited better strength and toughness due to a higher damage degree and more energy-consuming cracking mechanism. The above findings to a certain extent promote the future development of CZM in the field of concrete meso-mechanics.

The State of the Art and New Insight into Combined Finite–Discrete Element Modelling of the Entire Rock Slope Failure Process

The stability of rock slopes is of significance, as even the slightest slope failure can result in damage to infrastructure and catastrophes for human beings. Thus, this article focuses on the review of the current techniques available for rock slope stability analysis. The rock slope stability techniques can be classified as conventional methods and numerical methods. The advantages and limitations of the conventional method are briefly reviewed. The numerical methods mainly included three types, i.e., continuum methods, discontinuum methods, and the combined/hybrid continuum–discontinuum methods. This article pays more attention to the last type. The combined/hybrid finite–discrete element method (FDEM), which might be the most widely used continuum–discontinuum method, is introduced and we illustrated its abilities in modelling the entire rock slope failure process. The fundamental principles of FDEM, i.e., the contact interaction of the discrete bodies and the transition from continuum to discontinuum, are introduced in detail. The abilities of the FDEM in modelling the rock slope failure process are calibrated by modelling the entire typical rock slope failure process. Then, the application of the FDEM in the analysis of slope stability is introduced and discussed. Finally, the authors give insight into the GPGUP-parallelized FDEM modelling of the high rock slope failure process by the implementation of the strength reduction method (SRM). It is concluded that the FDEM can effectively model the entire rock slope failure process, even without the implantation of any slope modes, and the GPGUP-parallelized FDEM is a promising tool in the study and application of rock slope stabilities.

Optimal Modeling of an Elevator Chassis under Crash Scenario Based on Characterization and Validation of the Hyperelastic Material of Its Shock Absorber System

A wide variety of hyperelastic rubber-like materials, exhibiting strong nonlinear stress–strain relations under large deformations, is applied in various industrial mechanical systems and engineering applications involving shock and vibration absorbers. An optimal design procedure of an elevator chassis crashing on a hyperelastic shock absorber in a fail scenario, applicable in large-scale mechanical systems or industrial structures of high importance under strong nonlinear dynamic excitation, is presented in this work. For the characterization of the hyperelastic absorber, a Mooney–Rivlin material model was adopted, and a series of in-lab compression quasi-static tests were conducted. Applying a fully parallelizable state-of-the-art stochastic model updating methodology, coupled with robust, accurate and efficient Finite Element Analysis (FEA) software, the hyperelastic behavior of the shock absorber was validated under uniaxial large deformation, in order to tune all material parameters and develop a high-fidelity FE model of the shock absorber system. Next, a series of in situ full-scale experimental trials were carried out using a test-case elevator chassis, representing the crash scenario on the buffer absorber system, after a controlled free fall. A limited number of sensors, i.e., triaxial accelerometers and strain gauges, were placed at characteristic points of the real structure of the elevator chassis recording experimental data. A discrete Finite Element (FE) model of the experimentally tested arrangement involving the elevator chassis and updated buffer absorber system along with all boundary conditions was developed and used in explicit nonlinear analysis of the crash scenario. Steel material properties and the characterized updated Mooney–Rivlin material model were assigned to the elevator chassis and buffer, respectively. A direct comparison of the numerical and experimental data validated the reliability and accuracy of the methodology applied, whereas results of the analysis were used in order to redesign and optimize a new-design elevator chassis, achieving minimum design stresses and satisfying serviceability limit states.

Hybrid Finite-Discrete Element Modelling of Various Rock Fracture Modes during Three Conventional Bending Tests

The numerical techniques for modelling the rock fracture have been briefly reviewed. A hybrid finite-discrete element method (HFDEM) is proposed to simulate various fracture types of rock. A fracture model is implemented in the HFDEM for simulation of the three main fracture types. In addition, the influence of the strain rate is considered during the HFDEM modelling rock behavior. Then, two typical rock mechanism tests are employed to calibrate the HFDEM. The proposed method has well modelled the rock fracture processes and can obtain reasonable stress distribution and force–displacement curves. After that, the HFDEM is used to model three convention bending tests. The obtained rock fracture processes indicates that the HFDEM can simulate various fracture types. The obtained rock strengths and fracture toughness indicate that the HFDEM can reflect the influence of the strain rate. It is concluded that the HFDEM can model the entire and complete rock fracture process during the three convention bending tests, and it also can capture the rock’s behavior on the strain rate.

A finite-discrete element based appoach for modelling the hydraulic fracturing of rocks with irregular inclusions

A systematic hybrid approach for modelling the hydraulic fracturing process of heterogeneous rocks with irregular inclusions is developed. This approach is based on a series of computational algorithms, including Fourier series transformation, level-set-based overlapping detection, and the finite-discrete element method. Three major steps are included: (1) circular parameterization and Fourier transformation are employed to reproduce realistic inclusion contours with arbitrary irregular shapes; (2) a novel overlapping detection method based on a level-set function is employed to allocate irregular inclusions effectively and efficiently; and (3) the finite-discrete element model is established by integrating cohesive elements with pore pressure nodes into the solid mesh to simulate the progressive hydraulic fracture and interface crack of heterogeneous rocks. To validate the proposed hybrid approach, modelling results by the established model are compared with numerical simulations in the literature. In addition, the influences of injection speed and interface strength on the mechanical and fracturing responses of heterogeneous rocks are discussed. The results demonstrate that the proposed hybrid approach is capable of simulating the hydraulic fracturing process of heterogeneous rocks.

Coupled finite-discrete element modeling and potential applications in civil engineering

Since its appearance at the last of seventy decades, the Discrete Element Modeling (DEM) has been widely used in the modeling of geomaterials but regrettably limited to small scales problems by considering grains interactions. Recently, a new trend has emerged in combining DEM with other methods. The coupled approach allows extending the methods toward a wide range of civil engineering applications. Among them, FEM×DEM coupling has been the topic of research over the past decade. The FEM×DEM coupling has been mainly developed in two categories: direct interaction and multi-scale coupled models. In the first regard, this paper summarizes the basic principle of FEM and DEM, then reviews a number of possible direct coupling strategies between FEM and DEM together with potential applications in civil engineering. The second objective is to develop a model that combines these two above mentioned methods in a multi-scale approach. The results obtained by the developed model have been proved to efficiently tackle the complicated problem in engineering applications by assessing both macro and micro features and establishing the linking information between them.