Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

Investigation of FRP and SFRC Technologies for Efficient Tunnel Reinforcement Using the Cohesive Zone Model

Amid urbanization and the continuous expansion of transportation networks,the necessity for tunnel construction and maintenance has become paramount.Addressing this need requires the investigation of efficient,economical,and robust tunnel reinforcement techniques.This paper explores fiber reinforced polymer(FRP)and steel fiber reinforced concrete(SFRC)technologies,which have emerged as viable solutions for enhancing tunnel structures.FRP is celebrated for its lightweight and high-strength attributes,effectively augmenting load-bearing capacity and seismic resistance,while SFRC’s notable crack resistance and longevity potentially enhance the performance of tunnel segments.Nonetheless,current research predominantly focuses on experimental analysis,lacking comprehensive theoretical models.To bridge this gap,the cohesive zone model(CZM),which utilizes cohesive elements to characterize the potential fracture surfaces of concrete/SFRC,the rebar-concrete interface,and the FRP-concrete interface,was employed.A modeling approach was subsequently proposed to construct a tunnel segment model reinforced with either SFRC or FRP.Moreover,the corresponding mixed-mode constitutive models,considering interfacial friction,were integrated into the proposed model.Experimental validation and numerical simulations corroborated the accuracy of the proposed model.Additionally,this study examined the reinforcement design of tunnel segments.Through a numerical evaluation,the effectiveness of innovative reinforcement schemes,such as substituting concrete with SFRC and externally bonding FRP sheets,was assessed utilizing a case study from the Fuzhou Metro Shield Tunnel Construction Project.

Numerical simulation of the mechanical behavior of superconducting tape in conductor on round core cable using the cohesive zone model

Cables composed of rare-earth barium copper oxide(REBCO)tapes have been extensively used in various superconducting devices.In recent years,conductor on round core(CORC)cable has drawn the attention of researchers with its outstanding current-carrying capacity and mechanical properties.The REBCO tapes are wound spirally on the surface of CORC cable.Under extreme loadings,the REBCO tapes with layered composite structures are vulnerable,which can lead to degradation of critical current and even quenching of superconducting devices.In this paper,we simulate the deformation of CORC cable under external loads,and analyze the damage inside the tape with the cohesive zone model(CZM).Firstly,the fabrication and cabling of CORC are simulated,and the stresses and strains generated in the tape are extracted as the initial condition of the next step.Then,the tension and bending loads are applied to CORC cable,and the damage distribution inside the tape is presented.In addition,the effects of some parameters on the damage are discussed during the bending simulations.

Numerical study of fatigue damage of asphalt concrete using cohesive zone model

In order to investigate the fatigue behavior of asphalt concrete, a new numerical approach based on a bi-linear cohesive zone model （CZM） is developed. Integrated with the CZM, a fatigue damage evolution model is established to indicate the gradual degradation of cohesive properties of asphalt concrete under cyclic loading. Then the model is implemented in the finite element software ABAQUS through a user-defined subroutine. Based on the proposed model, an indirect tensile fatigue test is finally simulated. The fatigue lives obtained through numerical analysis show good agreement with laboratory results. Fatigue damage accumulates in a nonlinear manner during the cyclic loading process and damage initiation phase is the major part of fatigue failure. As the stress ratio increases, the time of the steady damage growth stage decreases significantly. It is found that the proposed fatigue damage evolution model can serve as an accurate and efficient tool for the prediction of fatigue damage of asphalt concrete.

Finite Element Simulations of the Localized Failure and Fracture Propagation in Cohesive Materials with Friction

Strain localization frequently occurs in cohesive materials with friction(e.g.,composites,soils,rocks)and is widely recognized as a fundamental cause of progressive structural failure.Nonetheless,achieving high-fidelity simulation for this issue,particularly concerning strong discontinuities and tension-compression-shear behaviors within localized zones,remains significantly constrained.In response,this study introduces an integrated algorithmwithin the finite element framework,merging a coupled cohesive zone model(CZM)with the nonlinear augmented finite elementmethod(N-AFEM).The coupledCZMcomprehensively describes tension-compression and compressionshear failure behaviors in cohesive,frictional materials,while the N-AFEM allows nonlinear coupled intraelement discontinuities without necessitating extra nodes or nodal DoFs.Following CZM validation using existing experimental data,this integrated algorithm was utilized to analyze soil slope failure mechanisms involving a specific tensile strength and to assess the impact of mechanical parameters(e.g.,tensile strength,weighting factor,modulus)in soils.

COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES

Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.

Failure simulation in resistance spot-welded lap-joints using cohesive zone modeling

This paper concentrates on simulating fracture in thin walled single-lap joints connected by resistance spot-welding(RSW)process which were subjected to tensile loading.For this purpose,three sets of lap-joints with different spot configurations were tested to achieve the joints’tensile behavior.To simulate the joints tensile behavior,firstly a 2D axisymmetric finite element(FE)model was used to calculate residual stresses induced during the welding process.Then the results were transferred to 3D models as pre-stress.In this step,cohesive zone model(CZM)technique was used to simulate fracture in the models under tensile load.Cohesive zone parameters were extracted using coach-peel and shear lap specimens.The results were employed to simulate deformation and failure in single lap spot weld samples.It has been shown that considering the residual stresses in simulating deformation and fracture load enables quite accurate predictions.

Delamination analysis of woven fabrication laminates using cohesive zone model

A new test method was proposed to evaluate the cohesive strength of composite laminates. Cohesive strength and the critical strain energy for Mode-II interlamiar fracture of E-glass/epoxy woven fabrication were determined from the single lap joint(SLJ) and end notch flexure(ENF) test, respectively. In order to verify their adequacy, a cohesive zone model simulation based on interface finite elements was performed. A closed form solution for determination of the penalty stiffness parameter was proposed. Modified form of Park-Paulino-Roesler traction-separation law was provided and conducted altogether with trapezoidal and bilinear mixed-mode damage models to simulate damage using Abaqus cohesive elements. It was observed that accurate damage prediction and numerical convergence were obtained using the proposed penalty stiffness. Comparison between three damage models reveals that good simulation of fracture process zone and delamination prediction were obtained using the modified PPR model as damage model. Cohesive zone length as a material property was determined. To ensure the sufficient dissipation of energy, it was recommended that at least 4 elements should span cohesive zone length.

A Modified Cohesive Zone Model for Simulation of Delamination Behavior in Laminated Composites

Considering the promotion effect of interlaminar normal tensile stress and the inhibition effect of interlaminar normal compressive stress,two kinds of elimination initial criteria were proposed in this paper.Based on these two delamination initial criteria,a modified cohesive zone model(CZM)was established to simulate the delamination behavior in laminated composites.Numerical simulations of double cantilever beam(DCB),mixed-mode bending(MMB)and end notched flexure(ENF)tests were conducted.The results show that the proposed model can do a better job than common ones when it is used to predict laminates’delamination under interlaminar compression stress.Moreover,a factor r,named cohesive strength coefficient,was defined in this paper on account of the difference between cohesive strength and interlaminar fracture strength.With changing factor r,it shows that a moderate variation of cohesive strength will not cause significant influences on global load-displacement responses.Besides,in order to obtain a good balance between prediction accuracy and computational efficiency,there shall be two or three numerical elements within the cohesive zone.

CRACK PROPAGATION IN POLYCRYSTALLINE ELASTIC-VISCOPLASTIC MATERIALS USING COHESIVE ZONE MODELS

Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones. Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals. The grain interior＇s material properties （e.g. strain rate sensitivity） characterize the competitions between plastic and cohesive energy dissipation mechanisms. The higher the strain rate sensitivity is, the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy, which delays the cohesive zone rupturing. With the strain rate sensitivity decreased, the material property tends to approach the elastic-plastic responses. In this case, the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding. Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries. Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.

Determination of key parameters of Al–Li alloy adhesively bonded joints using cohesive zone model

The key parameters of the adhesive layer of a reinforcing patch are of great significance and affect the ability to suppress crack propagation in an Al–Li alloy patch-reinforced structure.This paper proposes a method to determine the key parameters of the adhesive layer of adhesively bonded joints in the Al–Li alloy patch-reinforced structure.A zero-thickness cohesive zone model(CZM)was selected to simulate the adhesive layer’s fracture process,and an orthogonal simulation was designed to compare against the test results.A three-dimensional progressive damage model of an Al–Li alloy patch-reinforced structure with single-lap adhesively bonded joints was developed.The simulation’s results closely agree with the test results,demonstrating that this method of determining the key parameters is likely accurate.The results also verify the correctness of the cohesive strength and fracture energy,the two key parameters of the cohesive zone model.The model can accurately predict the strength and fracture process of adhesively bonded joints,and can be used in research to suppress crack propagation in Al–Li alloy patch-reinforced structures.

Determination of Key Cohesive Zone Model’s Parameters for Orthotropic Paper and Its Static Fracture Simulation

Investigation of paper cutting process is vital for the design of cutting tools,but the fracture mechanism of paper cutting is still unclear.Here,we focus on the cutting process of paper,including the key parameters of cohesive zone model(CZM)for the orthotropic paper,to simulate the shear fracture process.Firstly,the material constants of the orthotropic paper are determined by longitudinal and transverse tensile test.Secondly,based on the tensile stressstrain curves,combined with damage theory and numerical simulations,the key parameters of the CZM for the orthotropic paper are obtained.Finally,a model III fracture is simulated to verify the accuracy of the model.Results show that the load-displacement curves obtained by the simulation is consistent with the test results.

Finite element simulation of the micromachining of nanosized-silicon-carbide-particle reinforced composite materials based on the cohesive zone model

A finite element method based on the cohesive zone model was used to study the micromachining process of nanosized silicon-carbide-particle(SiCp) reinforced aluminum matrix composites. As a hierarchical multiscale simulation method, the parameters for the cohesive zone model were obtained from the stress-displacement curves of the molecular dynamics simulation. The model considers the random properties of the siliconcarbide-particle distribution and the interface of bonding between the silicon carbide particles and the matrix.The machining mechanics was analyzed according to the chip morphology, stress distribution, cutting temperature, and cutting force. The simulation results revealed that the random distribution of nanosized SiCp causes non-uniform interaction between the tool and the reinforcement particles. This deformation mechanics leads to inhomogeneous stress distribution and irregular cutting force variation.

IMPROVED COHESIVE ZONE MODEL AND ITS APPLICATION IN INTERFACE CONTACT ANALYSIS

An improved interface cohesive zone model is developed for the simulation of interface contact, under mixed-mode loading. A new debonding initiation criterion and propagation of debonding law, taking into account the pressure stress influence on contact shear strength, is proposed. The model is implemented in a finite-element program using subroutine VUINTER of ABAQUS Explicit. An edge-notch four-point bending process and laminated vibration damping steel sheet punch forming test are simulated with the improved model in ABAQUS Explicit. The numerical predictions agree satisfactorily with the corresponding experimental results.

Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

A Dugdale model based geometrical amplifier enables the measurement of separation-to-failure for a cohesive interface

Regardless of all kinds of different formulae used for the traction-separation relationship in cohesive zone modeling,the peak tractionσ_m and the separation-to-failureδ_0(or equivalently the work-to-separationΓ) are the primary parameters which control the interfacial fracture behaviors. Experimentally,it is hard to determine those quantities,especially forδ_0,which occurs in a very localized region with possibly complicated geometries by material failure.Based on the Dugdale model,we show that the separation-to-failure of an interface could be amplified by a factor of L/r_p in a typical peeling test,where L is the beam length and r_p is the cohesive zone size.Such an amplifier makesδ_0 feasible to be probed quantitatively from a simple peeling test. The method proposed here may be of importance to understanding interfacial fractures of layered structures,or in some nanoscale mechanical phenomena such as delamination of thin films and coatings.

3D Cohesive Finite Element Minimum Invasive Surgery Simulation Based on Kelvin‑Voigt Model

Minimally invasive surgery is an important technique used for cytopathological examination.Recently,multiple studies have been conducted on a three-dimensional(3D)puncture simulation model as it can reveal the internal deformation state of the tissue at the micro level.In this study,a viscoelastic constitutive equation suitable for muscle tissue was derived.Additionally,a method was developed to define the fracture characteristics of muscle tissue material during the simulation process.The fracture of the muscle tissue in contact with the puncture needle was simulated using the cohesive zone model and a 3D puncture finite element model was established to analyze the deformation of the muscle tissue.The stress nephogram and reaction force under different parameters were compared and analyzed to study the deformation of the biological soft tissue and guide the actual operation process and reduce pain.

Mesoscale Modeling of Hooked-End Steel Fiber Reinforced Concrete under Uniaxial Compression Using Cohesive Elements

Based on the cohesive zone model, the 2D mesostructures were developed for numerical studies of multi-phase hooked-end steel fiber reinforced concrete under uniaxial compression. The zero-thickness cohesive interface elements were inserted within the mortar, on interfaces of mortar and aggregates and interfaces of mortar and fibers to simulate the failure process of fiber reinforced concrete. The results showed that the numerical results matched well the experimental results in both failure modes and stress-strain behavior. Hooked-end steel fiber reinforced concrete exhibited ductile failure and maintained integrity during a whole failure process. Compared with normal concrete, HES fiber reinforced concrete was greater stiffness and compressive strength;the descending branch of the stress-strain curve was significantly flatter;the residual stress was higher.

Separation work analysis of cohesive law and consistently coupled cohesive law

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model （CZM） and the cohesive element method. The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models. Based on the proposed consistently coupled rule/principle, the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive law by analyzing the surface separation work. It is shown that the Xu-Needleman law is only valid in the mixed mode fracture when the normal separation work equals the tangential separation work. Based on the consistently coupled principle and the modification of the Xu-Needleman law, a consistently coupled cohesive （CCC） law is given. It is shown that the proposed CCC law has already overcome the non-consistency defect of the Xu-Needleman law with great promise in mixed mode analyses.

界面应力传递重新分析及Cohesive模型参数的确定

在经典剪滞理论中引入双线性cohesive模型表征纤维/基体之间的非理想界面,重新分析了纤维增强复合材料中的应力传递机理,得到了考虑界面因素的应力分布。用上述结果解释了单丝段裂实验过程中的现象,讨论了界面参数和材料性能对应力分布的影响。基于上述理论,建立了用cohesive单元表征界面的模拟单丝段裂实验的三维有限元模型,结合单丝段裂实验结果,提出了一种估测cohesive界面刚度参数的新方法。数值和理论分析结果与实验结果对比,吻合良好,可以为材料的界面性能分析和材料设计提供参考依据。