Finite-discrete Element Method Research Articles

An α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-Robust and Second-Order Accurate Scheme for a Subdiffusion Equation

We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order α∈(0,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\in (0,1)$$\\end{document}. The basic idea of our scheme is based on local integration followed by linear interpolation. It reduces to the standard Crank–Nicolson scheme in the classical diffusion case, that is, as α→1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\rightarrow 1$$\\end{document}. Using a novel approach, we show that the proposed scheme is α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-robust and second-order accurate in the L2(L2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2(L^2)$$\\end{document}-norm, assuming a suitable time-graded mesh. For completeness, we use the Galerkin finite element method for the spatial discretization and discuss the error analysis under reasonable regularity assumptions on the given data. Some numerical results are presented at the end.

Influence of weak interlayer thickness on mechanical response and failure behavior of rock under true triaxial stress condition

In this study, we meticulously investigate the influence of the thickness of weak interlayer on mechanical response and failure behavior of rock mass near the free surface of tunnel, with the aid of a true triaxial test system. We simulated the true triaxial stress condition of rock mass containing weak interlayer proximate to the excavation boundary, where one face remains free, while others are subjected to loading stress and increasing tangential stress. The experimental results reveal a distinct change in the fracture morphology near the free surface of rock mass as the thickness of weak interlayer increases, concomitant with a gradual decrease in the fractal dimension. With the increase of the thickness of weak interlayer, the failure characteristics of rock mass change from a “binary” to a “unitary” feature, i.e. mixed tension-shear failure near the free surface and shear failure far away from the free surface changes to mixed tension-shear failure that only occurs near the free surface. Moreover, an inverse relationship is observed between the bearing capacity of the rock mass and the thickness of weak interlayer. Conversely, the peak strain in the tangential stress direction increases with the increase of the thickness of weak interlayer, illustrating that the slip shear strain of rock block positioned above the weak interlayer is gradually formed, and governs the strain behavior of rock mass in the tangential stress direction with the increases of the thickness of weak interlayer. By employing the finite-discrete element method (FDEM), we replicated the failure process of surrounding rocks containing weak interlayers near the free surface of tunnel, demonstrating considerable congruity with our physical test results. In light of the failure characteristics of surrounding rocks containing weak interlayers, we advocated a localized area priority reinforcement support strategy, prioritizing regions with weak interlayers. Numerical simulations verified the effectiveness of this approach in controlling fracture proliferation in surrounding rocks and inhibiting the splitting failure of surrounding rocks containing weak interlayers near the free surface of tunnel.

An enhanced polar-based GPGPU-parallelized contact detection algorithm for 3D FDEM and its application to cracking analysis of shield tunnel segmental linings

This study introduces the three-dimensional combined finite-discrete element method (3D FDEM) to perform cracking analysis of segmental linings under extreme conditions. Considering the complex contact interactions of segments, this study first proposes a polar-based GPGPU-parallelized contact detection algorithm to handle memory issues confronted by existing FDEM algorithms. Initially, a spatial decomposition approach based on the polar coordinate system is implemented during the broad search phase. Each tetrahedral element is positioned within suitable search cells according to the axis-aligned bounding box. Subsequently, element pairs within each search cell are iteratively traversed, and potential contact pairs are identified using the judge cell criteria. After the broad search, a narrow search phase is executed to determine all real contacts. Following the above implementation, a load-structure model encompassing soil spring and external pressure calculations is then proposed. Based on the shape functions and coordinate transformation, the formulations of soil springs and external loads are derived and parallelized in the 3D FDEM framework. Three numerical tests are presented to validate the effectiveness of the proposed approach. Simulation results confirm the suitability of the proposed method for cracking analysis of segmental linings. Compared to the existing methods, it reduces GPU memory usage by 56 ∼ 76 % without extending time, which enhances the computational scale of 3D FDEM simulations. Furthermore, the proposed method is applied to two engineering scenarios, i.e., straight and curved segmental linings, both considering the absence and presence of contact defects between segments. The results show that contact defects can significantly reduce the resistance of the structural system comprising bolts and concrete segments for straight and curved scenarios.

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

Abstract In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Péclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Streamline Upwind Petrov–Galerkin technique is used in the optimality system to overcome these unpleasant effects. We will apply a finite element method discretization in an optimize-then-discretize approach. Concerning the parabolic case, a stabilized space-time framework will be considered and stabilization will also occur in both bilinear forms involving time derivatives. Then we will build Reduced Order Models on this discretization procedure and two possible settings can be analyzed: whether or not stabilization is needed in the online phase, too. In order to build the reduced bases for state, control, and adjoint variables we will consider a Proper Orthogonal Decomposition algorithm in a partitioned approach. It is the first time that Reduced Order Models are applied to stabilized parabolic problems in this setting. The discussion is supported by computational experiments, where relative errors between the FEM and ROM solutions are studied together with the respective computational times.

Numerical investigation of mechanical responses and failure features of coal measure strata using combined finite-discrete element method

Investigating the mechanical responses and failure features of the deep coal measure strata (CMS) is essential for designing hydraulic fracturing treatments and preventing geological dynamic hazards in underground engineering. In this paper, a three-dimensional CMS model is established by the combined finite-discrete element method (FDEM). The mechanical properties, stress evolutions and failure features of the CMS with different lithological combinations (sandstone-coal-sandstone (SCS), sandstone-coal-mudstone (SCM) and mudstone-coal-mudstone (MCM)) and thickness ratios are investigated under the uniaxial compressive condition. Results indicate that the SCS combination exhibits the highest uniaxial compressive strength (UCS) and elastic modulus, followed by the SCM and MCM combinations. The mechanical properties of the CMS are predominantly determined by the softer coal layer. The mechanical contrasts in elastic modulus and Poisson’s ratio between adjacent layers cause the generation of additional compressive stress in the softer layer and additional tensile stress in the stiffer layer. Therefore, the softer coal layer exhibits the shear-dominated failure pattern while the stiffer sandstone/mudstone layer displays the tensile-dominated failure pattern in the CMS. Furthermore, as the thickness ratio of the coal layer increases, the UCS, elastic modulus, and interfacial constraint stress decrease in the CMS. Additionally, the UCS and stress–strain relationship in the post-peak stage exhibit the noticeable size effect, whereas the mechanical behaviors in the pre-peak stage and the ultimate fracture patterns show the opposite. The elastic modulus and interfacial constraint stress obtained by the FDEM simulation match well with those calculated by theoretical models. The key findings of this paper can provide fundamental understanding and reliable parameters for multi-scale geomechanical modeling in petroleum and mining engineering.

Estimating the macro strength of rock based on the determined mechanical properties of grains and grain-to-grain interfaces

Obtaining complete rock cores is exceptionally challenging in certain extreme environments, such as deep earth and deep space; consequently, it is difficult to obtain the macro strengths of rock, which are the key indexes for engineering design, via standard rock mechanical tests. This research indicates that by determining and leveraging the mechanical properties of grains and grain-to-grain interfaces, the rock macro strength can be effectively estimated. Nanoindentation tests were first conducted to determine the elastic modulus of the mineral grains and their interfaces. Subsequently, symmetrical and anti-symmetrical four-point bending tests were executed to establish the statistical law governing interfacial tensile and shear fracture toughnesses. Furthermore, by employing the Dugdale–Barenblatt model and considering the oblique angular distribution of interfacial cracks, the corresponding tensile strength, shear strength, and friction parameter were derived. These meso‑mechanical parameters were then inputted into the 3D Finite-Discrete Element Method to estimate rock macro strength. And the numerical results were then compared with the results of standard uniaxial compression, direct tension, Brazilian splitting, and direct shear tests. The consistency observed between the predictions and experimental results attests to the validity of the proposed method.

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.

Effects of Geo-Stress and Natural Fracture Strength on Hydraulic Fracture Propagation in a Deep Fractured Tight Sandstone Reservoir.

Hydraulic fracturing technology has been widely used in the tight reservoir reconstruction. Unfortunately, with the deepening of mining depth and the increase of geo-stress, the propagation mechanism of medium-pressure fractures in the reservoir is significantly different from that of conventional shallow reservoirs. Based on the combined finite discrete element method, this paper conducts numerical simulation research on deep tight sandstone reservoirs in the west. The discrete fracture network modeling method is used to establish a tight sandstone reservoir model with natural bedding, and the influence of geo-stress difference and natural fracture strength on hydraulic fracture propagation law in a high geo-stress environment is discussed in detail. The results show that the difference between geo-stress and the strength of natural fractures has a significant effect on the shape and expansion of hydraulic fractures under the high geo-stress conditions. The greater the difference in ground stress, the more obvious the tendency of the main fractures of the reservoir, and the shorter the branch fractures. With the increase of natural fracture strength, the changes in propagation pressure, fracture length, area, and width, which can be fitted with a linear function with a goodness of fit as high as 0.99. In addition, the morphological results of hydraulic fractures in the simulation are not only affected by the constitutive parameters of the model but also may be affected by the randomness of the natural fracture network, thus, showing a certain degree of dispersion. Therefore, it is extremely necessary to build a reservoir fracturing model in a specific area based on more detailed geological monitoring data to guide actual construction. The above achievements have certain reference significance for the field operation of deep tight sandstone reservoirs.

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.

Numerical investigation of mode I fracture toughness anisotropy of deeply textured shale

The fracturing behavior of shale is controlled by the complex interaction between texture plane and rock matrix. This study develops a numerical model of semicircular bending of textured shale, integrating considerations of texture inclination and strength using the finite discrete element method, to examine the impact of shale anisotropy on damage patterns and fracture toughness. The results disclose the following insights: (1) Mode I fracture toughness anisotropy is significant, with fracture toughness showing a negative correlation with texture inclination and a positive correlation with texture strength. (2) Typical failure modes of SCB specimens encompass tensile failure across textured planes, tensile-shear mixed failure, tensile failure along texture planes, and tensile failure along the matrix. (3) For inclination angles ranging from 0° to 90°, cracks tend to deflect along the texture, leading to a fracture surface with high roughness. The fracture surface roughness was higher along the direction of maximum principal stress for the 0° and 90° specimens compared to the Divider specimens, while it was lower along the thickness direction compared to the Divider specimens. (4) The toughening mechanism of textured shales is categorized into three classes: separation along the texture, fracture path deflection, and texture cracking. Texture strength mainly influences texture cracking, while texture inclination primarily affects the deflection of crack paths and separation along the texture. (5) The criterion for predicting modified fracture toughness accurately predicts the anisotropic fracture toughness of shale compared to the conventional criterion for predicting fracture toughness.

Modeling the failure process of rock masses using a 3D nodal-based continuous-discontinuous deformation analysis method

A three-dimensional nodal-based continuous-discontinuous deformation analysis method (3D-NCDDAM) is developed in this study for modeling the failure process of rock masses. In the 3D-NCDDAM, four-node tetrahedral elements which can be automatally generated are used to discretize the problem domain. To reduce computational cost, and effectively model the failure process of rock masses at concerned regions, the problem domain is devided into two types of regions, namely, the “non-destructive region” and “possible destructive region”. The non-destructive region is mainly used to reduce the boundary effects on the numerical results, and is regarded transitional zone in which the failure of rock masses is not considered. For the possible destructive region, artificial joint elements are inserted, and the failure of these joint elements is used to represent fracture initiation and propagation in rock masses. Additionally, the contact potential which is initially proposed in finite-discrete element method (FDEM) is incorporated into the 3D-NCDDAM to simuate the opening and slipping of discontinuous structural planes involved in rock masses’ failure process. Note that the difficultly in determing contact types in the traditional 3D discontinuous deformation analysis (3D-DDA) method is avoided in the 3D-NCDDAM. The proposed 3D-NCDDAM can be treated as a hybrid method, which inherite both the advantage of DDA method and FDEM. To validate the 3D-NCDDAM, seven numerical examples are conducted. The numerical results indicte that the 3D-NCDDAM can effectively model the failure process of rock masses in both experimental scale and engineering scale.

Numerical investigation on the fracture and mechanical behaviors of marble containing two parallel fissures under triaxial compression conditions using FDEM

This paper aims to investigate the fracture and mechanical behaviors of fissured marble under triaxial compression. The two-dimensional models of marble with two parallel fissures and various rock bridge angles were established, and then the numerical simulations considering the effect of confining pressure were performed with the finite-discrete element method. The brittle-ductile transition and stress multi-peak characteristics are presented with the increase of the confining pressure. The characteristic strain, stress, and elastic strain energy exhibit various trends with the increment of the rock bridge angle, whilst increasing trend with the increment of the confining pressure. The cohesion presents the variation of first increasing and then decreasing with the increase of the rock bridge angle, and the friction angle presents the opposite trend to the cohesion. The proposed strength model can reflect the evolutions of the cohesion and the friction angle considering the effect of confining pressure and rock bridge angle. The elastic strain energy has the trends of nonlinear increase and fluctuation in the pre-peak and post-peak phases, respectively. The variation of kinetic energy is induced by the internal local fracture during the progressive failure. The failure pattern transforms from the tensile failure to the shear failure with the increase of the confining pressure. The coalescence behavior of cracks at the rock bridge can be classified into four modes.

A 3D discrete model for soil desiccation cracking in consideration of moisture diffusion

Soil desiccation cracking is a common phenomenon on the earth surface. Numerical modeling is an effective approach to study the desiccation cracking mechanism of soil. However, no three-dimensional (3D) model in the literature can consider the influence of desiccation cracking on moisture migration. To fill this gap, this work develops a novel 3D moisture diffusion discrete model that is capable of dynamically assessing the effect of cracking on moisture diffusion and allowing moisture to be discontinuous on both sides of the cracks. Then, the parametric analysis of the moisture exchange coefficient in the 3D moisture diffusion discrete model is carried out for moisture diffusion in continuous media, and the selection criterion of the moisture exchange coefficient for the unbroken cohesive element is given. Subsequently, an example of moisture migration in a medium with one crack is provided to illustrate the crack hindering effect on moisture migration. Finally, combining the 3D moisture diffusion discrete model with the finite-discrete element method (FDEM), the moisture diffusion-fracture coupling model is built to study the desiccation cracking in a strip soil and the crack pattern of a rectangular soil. The evolution of crack area and volume with moisture content is quantitatively analyzed. The modeling number and average width of cracks in the strip soil show a good consistency with the experimental results, and the crack pattern of the rectangular soil matches well with the existing numerical results, validating the coupled moisture diffusion-fracture model. Additionally, the parametric study of soil desiccation cracking is performed. The developed model offers a powerful tool for exploring soil desiccation cracking.

Numerical Investigation of Tree-Type Hydraulic Fracturing for Balanced Permeability Enhancement of Heterogenous Coal Seams Based on the Finite-Discrete Element Method Model

Numerical Investigation of Tree-Type Hydraulic Fracturing for Balanced Permeability Enhancement of Heterogenous Coal Seams Based on the Finite-Discrete Element Method Model

Capacity fading and inter/intra-granular fracture of polycrystalline cathode particle induced by charge/discharge cycles: A numerical study

The capacity fading of Lithium-ion batteries (LIBs) containing polycrystalline cathode materials can be attributed to the degradation of secondary particles caused by inter- and intra-granular fractures occurring during charging and discharging cycles. In this work, a diffusion-induced stress (DIS) analysis method based on the finite-discrete element method (FDEM) is developed for studying the fracture behaviors of polycrystalline cathodes. The analysis of lithiation and delithiation processes shows that C-rate and interfacial fracture toughness have significant effects on inter-granular crack morphologies. Our method enables precise analysis of the competition between intra- and inter-granular cracks and the effect of crack-impeded diffusion on crack morphologies. We compared numerical simulation results for scenarios where fracture toughness changes with the number of cycles, and demonstrated that the decreasing fracture toughness with cycle number is an important factor contributing to the slow crack growth. Additionally, we established the relationship between crack length and capacity loss, which agreed well with experimental results.

FDEM analysis of deep rock mass failure and its impact on horizontal bearing capacity in offshore wind turbine piles

Rock-socketed single piles are integral components of offshore wind turbine foundations in rock-based sea areas. Traditional numerical models have been employed to analyze the failure modes and lateral interactions between piles and the rock medium. However, these do not simulate the decline in the horizontal bearing capacity due to rock breakage, posing potential safety risks. In this study, the combined finite-discrete element method (FDEM) was used to simulate the deformation process of submarine rock masses transitioning from an intact to a fractured state. A notable innovation in the proposed approach is the consideration of the effects of the rock mass fracture and pile-rock cohesion on the load-bearing behavior of single-pile foundations. The FDEM model was validated through full-scale lateral load tests. The results showed a distinctive sequence in failure mechanisms, with the tensile failure of the rock mass around the pile at significant depths preceding the compression failure. Local failure at the contact interface significantly reduced the horizontal bearing capacity—a phenomenon that is inadequately represented by conventional finite element models. Furthermore, the cohesion element embedding method was introduced and used to simulate the influence of the tensile properties inherent in grouting materials on the failure strength and mode of the pile-rock interface. This study highlighted the importance of considering the nuanced effects of rock failure in the design of horizontally loaded piles. Failure to do so could lead to nonconservative designs and compromise the safety and efficacy of offshore wind turbine foundations. By pushing the boundaries of numerical modeling with the FDEM, the study aims to provide a more accurate and reliable framework for the design and assessment of rock-socketed single piles for offshore wind energy applications.

Numerical simulation study of PDC cutter rock breaking based on CT scanning to construct a rock model and apply a cohesive element to construct a discretization element

To more accurately simulate the interaction between a polycrystalline diamond compact (PDC) cutter and rock, the structural characteristics of basalt were analysed using computed tomography (CT), and a hard particle–matrix–pore three-phase rock model was established due to its structural characteristics. Three-dimensional models of the interaction between PDC cutters and rock were established by using the finite–discrete element method (FDEM). Using Voronoi diagrams to randomize the grid structure and optimize the propagation of cracks. This study revealed that a broken zone near the cutters will form during the rock breaking process, resulting in the affected area being larger than the area in contact with the formation rock. The rock breaking ability of circular cutters is stronger than that of conical cutters. When a conical cutter breaks hard particles, they are mainly striped or forced away from the rock, but circular cutters can divide hard particles into small pieces. The numerical model used in the research institute can effectively calculation results of the process of interaction between PDC cutter and rock, this proves that the application of the cohesive method to simulate rock breaking by PDC cutters is reliable.

A Hybrid Discrete-Finite Element method for continuous and discontinuous beam-like members including nonlinear geometric and material effects

This paper introduces a novel formulation, called Hybrid Discrete-Finite Element (HybriDFEM) method, for modelling one-directional continuous and discontinuous planar beam-like members, including nonlinear geometric and material effects. In this method, the structure is modelled as a series of distinct rigid blocks, connected to each other through contact pairs distributed along the interfaces. Each of those contact pairs are composed of two nonlinear multidirectional springs in series, which can represent either the deformation of the blocks themselves, or the deformation of their interface. Unlike the Applied Element Method, in which contact pairs are composed of one single spring, the current approach allows capturing phenomena such as sectional deformations or relative deformations between two blocks composed of different materials. This method shares similarities with the Discrete Element Methods in its ability to model contact interfaces between rigid or deformable units, but does not require a numerical time-domain integration scheme. More importantly, its formulation resembles that of the classical Finite Elements Method, allowing one to easily couple the latter with HybriDFEM. Following the presentation of its formulation, the method is benchmarked against analytical solutions selected from the literature, ranging from the linear-elastic response of a cantilever beam to the buckling and rocking response of continuous flexible columns, and rigid block stackings. One final example showcases the coupling of a HybriDFEM element with a linear beam finite element.

Numerical analysis of finite element method for a stochastic active fluids model

In this paper, we first investigate the well-posedness and regularity of mild solution to a stochastic active fluids model driven by the additive noise. A fully-discrete scheme is proposed for solving the given model, which is based on the finite element method for spatial discretization and the backward Euler method for temporal discretization. By overcoming the difficulty of error analysis caused by the discrete Laplacian operator, we obtain the convergence results of the developed scheme. Finally, some numerical examples are provided to validate the theoretical results and we also simulate the motion states of the active fluids.

Numerical study on flexural toppling failure of rock slopes using the finite discrete element method

Numerical study on flexural toppling failure of rock slopes using the finite discrete element method