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.

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.

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.

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.

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.

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。

Calibration of coupled hydro-mechanical properties of grain-based model for simulating fracture process and associated pore pressure evolution in excavation damage zone around deep tunnels

The objective of this paper is to develop a methodology for calibration of a discrete element grain-based model(GBM)to replicate the hydro-mechanical properties of a brittle rock measured in the laboratory,and to apply the calibrated model to simulating the formation of excavation damage zone(EDZ)around underground excavations.Firstly,a new cohesive crack model is implemented into the universal distinct element code(UDEC)to control the fracturing behaviour of materials under various loading modes.Next,a methodology for calibration of the components of the UDEC-Voronoi model is discussed.The role of connectivity of induced microcracks on increasing the permeability of laboratory-scale samples is investigated.The calibrated samples are used to investigate the influence of pore fluid pressure on weakening the drained strength of the laboratory-scale rock.The validity of the Terzaghi’s effective stress law for the drained peak strength of low-porosity rock is tested by performing a series of biaxial compression test simulations.Finally,the evolution of damage and pore pressure around two unsupported circular tunnels in crystalline granitic rock is studied.

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.

A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

3D打印混凝土界面力学行为及其对材料弹性常数影响的数值分析

应用复合材料细观力学分析理论,提出了基于界面模型的3D打印混凝土(3DPC)各向异性数值模拟方法,定量揭示了层、条界面力学行为及其对3DPC各向异性弹性常数的影响规律。采用界面单元和连续体单元相结合,模拟界面滑移开裂行为与基体的力学性能,设计单轴压缩、劈拉、十字交叉拉伸和斜剪试验确定模型所需参数及相应取值范围。结果表明:界面拉伸和剪切张力-位移曲线均呈双线性特征,条间界面强度总体高于层间;界面剪切行为在两个剪切主方向上无显著差异;条间和层间弹性模量对整体弹性模量具有线性影响,对整体泊松比具有指数函数影响,条间和层间界面剪切模量对整体剪切模量具有综合影响。

基于Roe-Siegmund循环内聚力模型焊趾疲劳裂纹萌生仿真

为建立焊趾疲劳裂纹萌生行为仿真方法,基于Roe-Siegmund循环内聚力模型对ABAQUS进行二次开发,形成用于反映疲劳累积损伤的VUMAT子程序,依据文献方法及试验数据获取Q345焊接区域材料的内聚力参数,通过Voronoi图法和内聚力单元法生成具有疲劳累积损伤特性和晶粒特征的微观模型,并与宏观对接焊缝模型合并,进行多尺度疲劳裂纹萌生仿真模拟,获得裂纹萌生路径、临界循环次数及晶粒力学响应特征.结果表明,此方法能够自发地选择符合实际情况的裂纹萌生位置以及短裂纹扩展路径,完成对焊接区域材料微观断裂过程的模拟,不同仿真组获取的临界循环次数存在于一定的分布范围内,模型中的累积内聚力长度需通过试验数据进行拟合.

基于内聚力模型的再生沥青混合料低温断裂性能研究

内聚力模型(CZM)在沥青混凝土开裂研究中得到了广泛应用,但采用内聚力模型对再生沥青混凝土断裂的研究还很少。本文采用随机算法和坐标控制法建立包含旧集料和新集料的再生沥青混合料半圆弯拉模型,将模型分为集料同分布模型和集料随机分布模型两类。研究-10℃时不同RAP掺量(0、25%、50%、75%、100%,质量分数)对再生沥青混合料SCB试件应力强度因子K_(IC)、断裂能G_(F)和抗裂指数I_(CR)的影响。研究结果表明:无RAP掺入的SCB试件具有较好的断裂性能;随着RAP掺量增大,应力强度因子K_(IC)、断裂能G_(F)和抗裂指数I_(CR)均减小,表明RAP的掺入会削弱沥青混合料的低温断裂性能;采用有限元模型得到的断裂参数与室内试验结果一致;相比于集料同分布模型,集料随机分布模型各评价指标的变异性系数整体更大,表明集料分布状态对开裂结果有一定影响;当计算样本足够多时,这两类模型获得的抗裂参数变化规律一致,可有效评价再生沥青混合料断裂性能。