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Failure of many brittle materials and structures can be modeled using interface‐oriented finite elements combined with intrinsic cohesive zone models. The discontinuous Galerkin (DG) finite element method provides an innovative framework for modeling brittle crack propagation with zero‐thickness interface elements, which can accommodate extrinsic cohesive laws to avoid the artificial compliance required in intrinsic cohesive models. However, robust formulations and implementations of DG methods are critical in alleviating the well‐known convergence issues for both crack nucleation and propagation with reduced instability. This paper presents a robust interface element formulation by modifying the incomplete interior penalty Galerkin (IIPG) method, which successfully avoids the initial element interface penetration across elements that occurs prior to crack nucleation, and thereby greatly reduces the instability issue as cracks open. We further verified and validated our implementation by using a bar tension test and a beam fracturing benchmark. The robustness of our proposed interface element method was demonstrated by a micromechanics fiber/matrix debonding problem with 64 fibers embedded in a bulk matrix. [ABSTRACT FROM AUTHOR]

The paper investigates the interaction of a steel striker with a three-layer target barrier. The barrier had three layers: ceramic, orthotropic organoplastic, and aluminum. The interaction velocity was 841 m/s, and the initial interaction angles with the barrier surface were set normal and 45°. The study is carried out numerically by the finite element method in a three-dimensional setting using the computer complex EFES developed by the authors. An elastic-brittle model is proposed to describe the behavior of the composite. A tensor-polynomial criterion of the second degree is used for the composite fracture. To describe the fracture of the orthotropic material of the target barrier, a two-stage model is proposed. The model of the composite behavior takes into account different strength moduli in compression and tension. As a criterion for the ceramics fracture, the deformation criterion was used. The behavior of the striker material and the metal layer are described by an elastoplastic medium, for the fracture of which a deformation criterion is proposed based on the limiting value of plastic deformation. The influence of the layer arrangement and initial interaction angle on the fracture of the target barrier has been studied. [ABSTRACT FROM AUTHOR]

We have discovered a peculiar form of fracture that occurs in a highly stretchable silicone elastomer (Smooth-On Ecoflex 00-30). Under certain conditions' cracks propagate in a direction perpendicular to the initial precut and in the direction of the applied load. In other words' the crack deviates from the standard trajectory and instead propagates perpendicular to that trajectory. The crack arrests stably, and thus the material ahead of the crack front continues to sustain load, thereby enabling enormous stretchabilities. We call this phenomenon "sideways" and stable cracking. To explain this behavior, we first perform finite-element simulations that demonstrate a propensity for sideways cracking, even in an isotropic material. The simulations also highlight the importance of crack-tip blunting on the formation of sideways cracks. Next, we provide a hypothesis on the origin of sideways cracking that relates to microstructural anisotropy (in a nominally isotropic elastomer). To substantiate this hypothesis, we transversely prestretch samples to various extents before fracture testing, as to determine the influence of microstructural arrangement (chain alignment and strain-induced crystallization) on fracture energy. We also perform microstructural characterization that indicates that significant chain alignment and strain-induced crystallization indeed occur in this material upon stretching. We conclude by characterizing how a number of loading conditions, such as sample geometry and strain rate, affect this phenomenon. Overall, this paper provides fundamental mechanical insight into basic phenomena associated with fracture of elastomers. [ABSTRACT FROM AUTHOR]

This paper presents a composite element algorithm of coupled normal stress and fluid flow process for fractured rock mass, developed from the composite element method (CEM). The coupled relation between the fracture flow and normal stress makes use of the 'filled model', which examines the asperities in the fracture as a layer of granular medium having high porosity and being clipped by the two parallel plates. The existence of fractures is not considered in the mesh generation, but it will be considered explicitly in the mapped composite element. The coupled normal stress and fluid flow process has been simulated by applying a cross iterative algorithm between the two fields. The proposed algorithm considers not only the flow through the fractures, but also the flow exchange between fractures and the surrounding rock blocks. In addition, it can be used for both the filled and non-filled fractures. The verification of the proposed algorithm has been conducted through the illustration of three examples by comparison with the conventional finite element method (FEM), from which the advantages and reliability of the proposed algorithm have been shown clearly. [ABSTRACT FROM AUTHOR]

Devices in modern technologies often have complex architectures, dissimilar materials, and small features. Their long-term reliability relates to inelastic, time-dependent mechanical behavior of such structures. This paper analyzes a three-layer structure consisting of, from top to bottom, an elastic film, a power-law creep underlayer, and a rigid substrate. The layers are bonded. Initially, the film is subject to a uniform biaxial tensile stress. A channel crack is introduced in the elastic film. As the underlayer creeps, the stress field in the film relaxes in the crack wake, but intensifies around the crack tip. We formulate nonlinear diffusion-like equations that evolve the displacement field. When the crack is stationary, the region in which the stress field relaxes increases with time. We identify the length scale of the region as a function of time. The stress intensity factor is proportional to the square-root of the length scale. For the power-law creep underlayer, this newly identified length depends on the film stress, and corrects an error in a previous paper by Huang, Prévost and Suo (Acta Materialia50, 4137, 2002). When the crack advances, its velocity can reach a steady state. We identify the scaling law for the steady velocity. An extended finite element method (X-FEM) is used to simultaneously evolve the creep strain and crack length. Numerical results are presented for the stress intensity factors of stationary cracks, and the steady velocities of advancing cracks. [ABSTRACT FROM AUTHOR]

Geologic fractures such as joints, faults, and slip surfaces govern the stability and performance of many subsurface systems in the built environment. As such, a variety of approaches have been developed for computational modeling of geologic fractures. Yet none of them lends itself to a straightforward utilization with the classical finite element method widely used in practice. Over the past decade, phase-field modeling has become a popular approach for simulating fracture, because it can be implemented simply with the standard finite element method without any surface-tracking algorithms. However, the standard phase-field formulations do not incorporate several critical features of geologic fractures, including frictional contact, pressure-dependence, quasibrittleness, mode-mixity, and their combined impacts on cracking. This article provides a brief report of a novel phase-field model that incorporates these features of geologic fractures in a well-verified and validated manner. Remarkably, the phase-field model allows one to simulate the combination of cohesive tensile fracture and frictional shear fracture without any algorithms for surface tracking and contact constraints. It is also demonstrated how phase-field modeling enables us to gain insights into geologic fractures that are challenging to investigate experimentally. [ABSTRACT FROM AUTHOR]

We extend the applicability of the embedded unit cell (EUC) method to three-dimensional (3D) fracture problems, which are modeled by the extended finite element method (XFEM). The EUC method is a concurrent multiscale method based on the computational homogenization theory for nonperiodic domains. Herein, we show that this method can accurately estimate fracture parameters and, in particular, stress intensity factors using the J-integral method. Additionally, the method is shown to capture crack propagation within the microscale domain, as well as cracks initiating at the microscale and propagating outwards onto the macroscale through the internal subdomain boundaries. To demonstrate the accuracy, robustness, and computational efficiency of the proposed method, several 3D numerical benchmark examples, including planar cracks with single and mixed-mode fractures, are considered. In particular, we analyze horizontal, inclined, square, and penny-shaped cracks embedded in a homogeneous material. The results are verified against full FEM models and known analytical solutions if available. Practical Applications: The insights of this research offer practical application for engineers and scientists in designing more resilient and durable structures. By extending the EUC method to 3D fracture problems, the study addresses the ability to forecast and access fracture phenomena in materials. This method is shown to be an effective approach for exploring the interaction between local microscopic discontinuities and cross-scale crack propagation, crucial for evaluating the durability of engineering structures. The EUC approach, integrated with XFEM, provides a comprehensive methodology for analyzing different fracture scenarios, including stationary mixed-mode cracks and crack-propagation examples. Its ability to accurately transition from microscale to macroscale analysis without remeshing introduces a valuable computational advantage, making it a more cost-efficient solution in fracture analysis. This research's application offers tangible benefits in industrial context, especially in aerospace, automotive, and construction industries, where precise evaluation of structure and material failure can lead to more cost-efficient and safer designs by reducing the maintenance costs and failure risks. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a novel formulation of a cohesive zone model able to effectively approximate the time-and temperature-dependent fracture process along a defined interface. The formulation relies on the assumption that the relaxation behavior of the traction is the origin of the time effects, and time temperature equivalence principle can be introduced in solving the temperature effects. A series basic hypotheses are introduced according to the previous research work and will be complied in the paper. By connecting N Maxwell models in parallel and letting the time-independent traction calculated by PPR cohesive zone model as the input parameter, the time-dependent traction will be output by numerical integration. Reduced time considering the effects of temperature will replace the real time in the numerical integration. With the tool of the user subroutine element, the novel formulation is implemented in FEM code ABAQUS. Typical load cases including constant tensile test and relaxation test are analyzed to illustrate the special properties of the formulation. With three set of input parameters, the proposed model can be utilized in a wide range of applied loading rates and temperatures as validated by the remarkable agreement with the experimental data in the case of the double sandwich cantilever beam made of solid propellant/insulation adherents bonded along the liner interface. Highlights • A novel time-and temperature-dependent cohesive model is proposed in this paper. • With the numerical integration, the proposed time-and temperature-dependent cohesive model is implemented in the FEM code ABAQUS. • A typical debonding interface between solid propellant and insulation is modeled and analyzed using the inversed model parameters. • The proposed model can deal with the unsteady loading rate and changed temperature which the aforementioned models unable to cope with. [ABSTRACT FROM AUTHOR]

The size effect on the mechanism of fracture in ultrafine grained sheets is an unsolved problem in microforming. This paper describes a tensile test carried out to study the fracture behavior and the shear fracture angles of both rolled and aged ultrafine grained aluminum 6061 sheets produced by asymmetric cryorolling. A scanning electron microscope was used to observe the fracture surface. The finite element method was used to simulate the tensile test using the uncoupled Cockcroft–Latham and Tresca criteria and the coupled Gurson–Tvergaard–Needleman damage criterion. It was found that the shear fracture angle decreases gradually from 90° to 64° with an increasing number of passes. The results of simulations using the Gurson–Tvergaard–Needleman criterion show trends similar to the experimental ones. The paper also presents a discussion on the fracture mechanism and the size effect during the tensile test. [ABSTRACT FROM PUBLISHER]

In this paper, by introducing a chemical field, the J-integral formulation is presented for the chemo-mechanical coupled medium based on the laws of thermodynamics. A finite element implementation of the J-integral was performed to study the mode I chemo-mechanical coupled fracture problem. For derivation of the coupled J-integral, the equivalent domain integral (EDI) method was applied to obtain the mode I J-integral, with expression of the area integrals based on constitutive relationships of a linear elastic small deformation for chemo-mechanical coupling, instead of the finite deformation problem. A finite element procedure is developed to compute the mode I J-integral, and numerical simulation of the y-direction stress field is studied by a subroutine UEL (User defined element) developed in ABAQUS software. Accuracy of the numerical results obtained using the mode I J-integral was verified by comparing them to a well-established model based on linear elastic fracture mechanics (LEFM). Furthermore, a numerical example was presented to illustrate path-independence of the formulated J-integral for a chemo-mechanical coupled specimen under different boundary conditions, showing a high accuracy and reliability of the present method. The variation laws of J-integral and the y-direction stress field with external chemical, mechanical loading and time are revealed. The J-integral value increases with larger external concentration loading in the same integral domain. The extent of diffusion is much greater with larger concentration, which leads to a stronger coupling effect due to the chemical field. This work provides new insights into the fracture mechanics for the chemo-mechanical coupled medium. [ABSTRACT FROM AUTHOR]

Modelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent discontinuities or cracks. On the other hand, discontinuous methods, as the cohesive zones, which model the crack propagation behaviour, are suited to represent the localised damaging process. However, they are unable to represent diffuse damage. Moreover, most of the cohesive models do not capture triaxiality effect. In this paper, the advantages of the two approaches are combined in a single damage to crack transition framework. In a small deformation setting, a nonlocal elastic damage model is associated with a cohesive model in a discontinuous Galerkin finite element framework. A cohesive band model is used to naturally introduce a triaxiality-dependent behaviour inside the cohesive law. Practically, a numerical thickness is introduced to recover a 3D state, mandatory to incorporate the in-plane stretch effects. This thickness is evaluated to ensure the energy consistency of the method and is not a new numerical parameter. The traction-separation law is then built from the underlying damage model. The method is numerically shown to capture the stress triaxiality effect on the crack initiation and propagation. [ABSTRACT FROM AUTHOR]

Purpose |!|#8211; The purpose of this paper is to present a numerical simulation of the hydrogen atomic effect on the steels fracture toughness, as well as on crack propagation using fracture mechanics and continuous damage mechanics models. Design/methodology/approach |!|#8211; The simulation was performed in an idealized elastic specimen with an edge crack loaded in the tensile opening mode, in a plane strain state. In order to simulate the effect of hydrogen in the steel, the stress intensity factor ahead of the crack tip in the hydrogenated material was obtained. The damage model was applied to simulate the growth and crack propagation being considered only two damage components: a mechanical damage produced by a static load and a non-mechanical damage produced by the hydrogen. Findings |!|#8211; The simulation results showed that the changes in the stress field at the crack tip and the reduction in the time of growth and crack propagation due to hydrogen effect occur. These results showed a good correlation and consistency with macroscopic observations, providing a better understanding of the hydrogen embrittlement phenomenon in steels. Originality/value |!|#8211; The paper attempts to link the concepts of the continuous damage and fracture mechanics to achieve a better approach in the representation of the physical phenomenon studied, in order to obtain a more accurate simulation of the processes involved. [ABSTRACT FROM AUTHOR]

This paper presents a generalized finite element method (GFEM) for crack growth simulations based on a two-scale decomposition of the solution-a smooth coarse-scale component and a singular fine-scale component. The smooth component is approximated by discretizations defined on coarse finite element meshes. The fine-scale component is approximated by the solution of local problems defined in neighborhoods of cracks. Boundary conditions for the local problems are provided by the available solution at a crack growth step. The methodology enables accurate modeling of 3-D propagating cracks on meshes with elements that are orders of magnitude larger than those required by the FEM. The coarse-scale mesh remains unchanged during the simulation. This, combined with the hierarchical nature of GFEM shape functions, allows the recycling of the factorization of the global stiffness matrix during a crack growth simulation. Numerical examples demonstrating the approximating properties of the proposed enrichment functions and the computational performance of the methodology are presented. [ABSTRACT FROM AUTHOR]

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, Smax/δ0. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from `complete slip before opening' to `opening in mode I before mode II shear offset'. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on computing the lower and upper bounds on stress intensity factors in elastic fracture mechanics with an efficient finite element output bound procedure on quantities of interest in engineering. The bounds procedure is obtained by minimizing the quadratic energy functional of output with constraints of equilibrium conditions of mechanics and continuity conditions of finite element space. The computation is based on solving the elemental Neumann residual problems for the bounds on energy norm of error in finite element solutions. The lower and upper bounds on the intensity factors of an open mode and a shear mode elastic fracture problems are computed in this paper. [ABSTRACT FROM AUTHOR]

This paper presents a micromechanical analysis of the influence of fiber–matrix interface fracture properties on the transverse tensile response of fiber-reinforced composite. The method combines three-dimensional (3D) computational micromechanics and augmented finite element method to provide high-fidelity results of damage initiation and propagation. Random arrangement of fibers and normal distribution of interface toughness and strength are considered in representative volume elements to capture the stochastic behavior of the composite under loading. Sensitivity analysis with respect to the interface properties distribution, and shape and size of fibers on the representative volume element’s strength are performed. The effect of fiber volume fractions on the strength and elastic modulus of the composite is investigated. Failure path in different representative volume elements are compared. The results show that the response of a representative volume element with identical interface properties overestimates the composite’s transverse strength. It is also shown that the damage initiation and propagation locations are affected by the distributions of fracture properties, and the shape and size of fibers within the representative volume element. [ABSTRACT FROM AUTHOR]

We in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures. The key idea is to develop a general refinement algorithm based on a so-called polytree mesh structure. The method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones, which are considered as special cases. Also, polytree meshes are conforming and can be regarded as a generalization of quadtree meshes. For the aim of this paper, we restrict our main interest in plane-strain limit analysis to von Mises-type materials, yet its extension to a wide class of other solid mechanics problems and materials is completely possible. To avoid volumetric locking, we propose an approximate velocity field enriched with bubble functions using Wachspress coordinates on a primal-mesh and design carefully strain rates on a dual-mesh level. An adaptive mesh refinement process is guided by an L 2 -norm-based indicator of strain rates. Through numerical validations, we show that the present method reaches high accuracy with low computational cost. This allows us to perform large-scale limit analysis problems favorably. [ABSTRACT FROM AUTHOR]

The present paper deals with an analytical description and FEM modeling of stress fields at the tip of a sharp rigid inclusion located on the bimaterial interface. In the asymptotic solutions obtained, modified stress intensity factors appear, which allow one to take into account the oscillatory singularity of occurring stress fields. Values of these factors are found using a FEM simulation combined with two probabilistic methods: extrapolation and approximation. Calculations are carried out for normal and shear loads. [ABSTRACT FROM AUTHOR]

• Quantified the effect of Hill anisotropic plasticity on J-Q characterization of semi-circular surface cracks. • Demonstrated that the isotropic and anisotropic J – Q parameters can significantly diverge, especially, when crack planes are misaligned with respect to the material coordinate system. • The results are important for providing accurate predictions of failure in pipeline steels that often show significant plastic anisoptropy. In this paper, the J - Q two-parameter characterization of Hill-anisotropic elastic–plastic crack-front fields are examined for surface cracked plates under uniaxial tensile loadings. A method for two-parameter characterization crack-front field in anisotropic plastic materials is presented. Extensive three-dimensional elastic–plastic finite element analyses were performed for semi-circular surface cracks in a finite thickness plate, under remote uniaxial tension loading conditions. Surface cracks with relative depths a / t = 0.2, 0.6 were investigated. The loading levels spanned from small-scale to large-scale yielding. Different crack orientations with respect to the material coordinate directions were also considered. In topological planes perpendicular to the crack front, the crack-front stress fields were obtained. In order to facilitate the determination of Q -factors, modified boundary layer analyses were also conducted. The modified boundary layer analyses were adapted to account for plastic anisotropy. The J - Q two-parameter approach was then used in characterizing the elastic–plastic crack-front stress fields along these 3D crack fronts. Complete distributions of the J -integral and Q -factors for a wide range of loading conditions were obtained. The results indicate that the J – Q characterization is applicable to Hill-anisotropic plastic materials and provides good estimate for the crack-front constraint loss experienced under large-scale yielding. It was also observed that the isotropic and anisotropic J – Q parameters can significantly diverge, especially, when crack planes are misaligned with respect to the material coordinate system. This highlights the importance of the consideration of plastic anisotropy when performing constraint-based fracture mechanics analyses. [ABSTRACT FROM AUTHOR]

This article discusses the numerical modeling of fracture processes in elastic-brittle bodies with statistically distributed subregions strength values. The authors propose a boundary value problem formulation and a solution algorithm using the finite element method. The study focuses on the distribution range and stress concentration influence on the fracture process. The results of numerical experiments show the significant influence of finite element properties distribution and stress concentration on the modeling results. The proposed approach considers the strength properties' statistical distribution and can be applied to the fracture modeling of inhomogeneous structures. The article also includes a list of references to various scientific articles related to the modeling and analysis of crack growth and failure behavior in different materials and structures. Additionally, the article titled "Ductile-brittle transition by varying structural size" explores the relationship between structural size and the transition from ductile to brittle behavior in materials. The authors conducted experiments and analyzed the fracture mechanics of different materials to understand how changes in size affect their mechanical properties. The findings suggest that smaller structures tend to exhibit more brittle behavior, while larger structures are more ductile. This research provides valuable insights into the behavior of materials under different conditions and can be useful for engineers and researchers studying fracture mechanics. [Extracted from the article]

The development of a parallel version of the fracture model dedicated for multi-phase materials based on a combination of the finite element model and random cellular automata approach is the overall goal of this study. Dual-phase (DP) steel, commonly used in the automotive industry, is selected as a case study for the present investigation. Firstly, various fracture modes that can occur during deformation in DP steel grade microstructures are presented from an experimental point of view. To consider explicitly microstructure features that play a significant role during initiation and subsequent failure propagation, the digital material representation concept is used. Then, details of the developed random cellular automata model, fully embedded within the finite element framework, are discussed. The cellular automata space definition, internal variables, state variables and transition rules replicating investigated fracture modes are presented in detail and discussed. The concept of data transfer and parallelization based on the Message Passing Interface methodology in such an innovative hybrid numerical model is also clearly presented. The final section of the paper is devoted to examples of obtained results highlighting model predictive capabilities. [ABSTRACT FROM AUTHOR]

In recent years, there has been new interest in understanding the mechanical failures of the polymer-composites used for fairing the hull and the superstructure of large vessels. On average, around 200 superyachts are launched every year, with about 50% of them presenting failures in their polymer-composite coating schemes. Very little literature data is available in understanding the fracture response of these materials for this particular application. This paper presents a numerical study on the flexural behaviour of three popular particulate polymer-composite materials used as coatings on megayacht vessels using the extended finite element method in Abaqus®. The numerical results have been validated against experiments carried out by the authors and good correlation has been obtained. The use of the correct mechanical properties obtained from mechanical testing of the bulk materials, has yielded accurate predictions of the flexural characteristics of the composite-steel specimens up to failure. Three different coating systems have been evaluated with the methodology outlined in this paper. This study demonstrates that validation of the numerical methods with experimental results creates the opportunity for the development of more parametric studies with a reduced requirement to conduct physical tests. The numerical results correlate well with the experimental results carried out by Prodromou [1]. The failure loads were predicted with an accuracy of 20% maximum difference from experiments whereas the deformation was predicted within a range of 12% maximum difference from experimental values. (Differences in the failure analysis results could be attributed to the varying properties of the polymer test coupons, however, validation provides encouraging results). Parameters such as the effect of thickness and the differing properties of the polymer-composites have been discussed. It has been found that coated coupons of low thickness can perform better in terms of deflection, thus reducing the probability of failure in real application. The increase in coating thickness leads to an increase in load carrying capacity and flexural rigidity of the beam as expected. Increased thickness of coating could increase surface stresses hence lead to earlier occurrence of cracking. The modelling procedure captured with accuracy the failure response of the composite under quasi-static loading conditions. • Establishment of the mechanical response of polymer-composite materials used as coatings on megayacht structures. • Development of numerical model capable of accurately predicting fracture in polymer-composite materials. • Validation of numerically obtained results using the extended finite element method with experimental results. • Influence of increased thickness in polymer-composite coatings used on steel substrates. [ABSTRACT FROM AUTHOR]

A new adaptive multiscale method for the non-linear fracture simulation of heterogeneous materials is proposed. The two major sources of errors in the finite element simulation are discretization and modelling errors. In the failure problems, the discretization error increases due to the strain localization which is also a source for the error in the homogenization of the underlying microstructure. In this paper, the discretization error is controlled by an adaptive mesh refinement procedure following the Zienkiewicz–Zhu technique, and the modelling error, which is the resultant of homogenization of microstructure, is controlled by replacing the macroscopic model with the underlying heterogeneous microstructure. The scale adaptation criterion which is based on an error indicator for homogenization is employed for our non-linear fracture problem. The control of both discretization and homogenization errors is the main feature of the proposed multiscale method. [ABSTRACT FROM PUBLISHER]

This paper provides a comparison between one particular phase-field damage model and a thick level set (TLS) damage model for the simulation of brittle and quasi-brittle fractures. The TLS model is recasted in a variational framework, which allows comparison with the phase-field model. Using this framework, both the equilibrium equations and the damage evolution laws are guided by the initial choice of the potential energy. The potentials of the phase-field model and of the TLS model are quite different. TLS potential enforces a priori a bound on damage gradient whereas the phase-field potential does not. The TLS damage model is defined such that the damage profile fits to the one of the phase-field model for a beam of infinite length. The model parameters are calibrated to obtain the same surface fracture energy. Numerical results are provided for unidimensional and bidimensional tests for both models. Qualitatively, similar results are observed, although TLS model is observed to be less sensible to boundary conditions. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The current paper aimed to model failures and fractures in single-lap bolted joints of woven fabric kenaf fiber reinforced polymer (KFRP) composite plate to fail in net-tension. The approach was based on the assumptions that micro-damage events were densely concentrated ahead of the notch tip and crack growth were readily seen along net-tension plane in a self-similar fashion. A 3-D finite element modelling framework were developed to explicitly incorporate bolt clamp-up in a range of KFRP series following tested experimental datasets. Lay-up types, normalized W/d, temperature exposure with constant bolt torque of 5 Nm were considered. It was found that KFRP plates under elevated temperature were stronger than under room temperature due to matrix toughening. Traction-separation relationship was incorported within Extended Finite Element Method (XFEM) framework to model damage within KFRP composite plate by using independent experimental datasets, here incorporates un-notched plate strength, so and fracture toughness, Gc of all testing lay-ups. Constitutive model used is associated with stress concentration, therefore good agreement between predicted and experimental bearing stress at failure with net-tension failure mode is perhaps not suprising. [ABSTRACT FROM AUTHOR]

This paper aims to contribute to the three-dimensional generalization of numerical prediction of crack propagation through the formulation of finite elements with embedded discontinuities. The analysis of crack propagation in two-dimensional problems yields lines of discontinuity that can be tracked in a relatively simple way through the sequential construction of straight line segments oriented according to the direction of failure within each finite element in the solid. In three-dimensional analysis, the construction of the discontinuity path is more complex because it requires the creation of plane surfaces within each element, which must be continuous between the elements. In the method proposed by Chaves (2003) the crack is determined by solving a problem analogous to the heat conduction problem, established from local failure orientations, based on the stress state of the mechanical problem. To minimize the computational effort, in this paper a new strategy is proposed whereby the analysis for tracking the discontinuity path is restricted to the domain formed by some elements near the crack surface that develops along the loading process. The proposed methodology is validated by performing three-dimensional analyses of basic problems of experimental fractures and comparing their results with those reported in the literature. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is the development of a method to predict interfacial failure in adhesive joints. The main originality of the paper resides on the application of a twofold criterion involving stress and energy conditions simultaneously to predict adhesive failure onset in different geometries of adhesive joints subjected to diverse loadings. Butt joints and double lap joints made of linear elastic materials are tested in torsion and tension. The failure onset predictions are based on finite element calculations and a twofold criterion which considers a novel stress condition. These predictions are accurate and prove the validity of the method to predict adhesive failure for different adhesive joint configurations and loadings. [Copyright &y& Elsevier]

This paper investigates linear-elastic response of cracked functionally graded layers subjected to thermomechanical loading; classical coupled thermoelastic equations are used in the calculations. The coupled dynamical system of equations obtained from the extended finite element discretization is solved by the Newmark method in the time domain. Micromechanical models for conventional composites are used to estimate properties of functionally graded layer. The interaction integral is then employed to calculate the stress intensity factors at each time step. In addition, crack propagation phenomenon under thermomechanical shocks is investigated in this paper. We have used MATLAB software to implement the algorithm and related code of problem. [ABSTRACT FROM AUTHOR]

This paper presents a quasi-static multiscale computational model with its verification and rational applications to mechanical behavior predictions of asphaltic roadways that are subject to viscoelastic deformation and fracture damage. The multiscale model is based on continuum thermo-mechanics and is implemented using a finite element formulation. Two length scales (global and local) are two-way coupled in the model framework by linking a homogenized global scale to a heterogeneous local scale representative volume element. With the unique multiscaling and the use of the finite element technique, it is possible to take into account the effect of material heterogeneity, viscoelasticity, and anisotropic damage accumulation in the small scale on the overall performance of larger scale structures. Along with the theoretical model formulation, two example problems are shown: one to verify the model and its computational benefits through comparisons with analytical solutions and single-scale simulation results, and the other to demonstrate the applicability of the approach to model general roadway structures where material viscoelasticity and cohesive zone fracture are involved. [ABSTRACT FROM AUTHOR]

A numerical model of ballistic impact on a two-dimensional Kevlar KM2® plain-woven fabric has been validated by experiment. This paper shows that it is necessary to experimentally measure material constants of yarns for having good input parameters of the model. Effects of yarn Poisson’s ratio, transverse and shear modulus on impact behaviors of a simple crimped yarn and a complete fabric have been carried out. The effect of the Poisson’s ratio can be negligible in both impact cases: on a single crimped yarn and a complete fabric. The same conclusion has been proven for the effect of the transversal modulus except the cases of its so low values that can cause yarn early damage. The shear modulus of a yarn appears to be an important material parameter that mainly influences the ballistic performance of a two-dimensional plain-woven fabric. When using a very high value of a shear modulus of yarn, a crimped single yarn is broken immediately after contact with projectile in pure shearing mode. [ABSTRACT FROM PUBLISHER]

ABSTRACT Specimen J-R curve is extensively used for structural integrity of large components. It is well known that J-R curve heavily depends on constraint level ahead of crack tip in remaining ligament. In earlier work, it was demonstrated that J-R curve from Three Point Bending (TPB) specimen is transferable to straight pipe with circumferential through wall crack. In this paper, the transferability of J-R curve is investigated from TPB specimen to pipe with circumferential surface crack. A 16 in. diameter pipe with circumferential surface crack and TPB specimen machined from same piping material (SA333Gr6 Steel) are tested. Consequently, 3D finite element analysis (FEA) has been performed on surface cracked pipe and TPB specimen. Crack-initiation load is also predicted for surface cracked pipe by FEA and compared with experimental result. J-R curve is calculated for the pipe using experimental data, that is, load, load line displacement and crack growth. J-R curve of pipe is compared with TPB specimen and it is found that the pipe is predicting much higher J-R curve than TPB. This difference of J-R curve is investigated by evaluating stress triaxiality in remaining ligament for both cases. Stress triaxiality is quantified using triaxiality factor ( h) ahead of crack tip for pipe and TPB specimen. It is found that the TPB specimen has considerably higher constraint level than pipe with surface crack, which is well supported by trend of J-R curves for specimen and pipe. A study has also been carried out to investigate the effect of internal pressure on the stress triaxiality. It is found that there is negligible difference in stress triaxiality because of internal pressure. The stress triaxiality is re-established as a qualitative parameter to assess the transferability of J-R curve from specimen to component. [ABSTRACT FROM AUTHOR]

This paper presents an effective numerical approach for dynamic brittle crack growth problems implemented on singular edge-based smoothed finite element method (sES-FEM). Both the consistent and lumped mass matrices are developed for five-node crack-tip elements for dynamic cases and their effects are compared on the numerical results. Further, to minimize the energy introduced or dissipated during continuous mesh rezoning, a balance recovery method is utilized in the computation. The interaction integral method is used to evaluate mixed dynamic stress intensity factors. Several numerical examples are presented to demonstrate the accuracy and applicability of the present approach in modeling dynamic crack propagation. The numerical results are examined in detail by comparisons with analytical solutions or experimental results, which shows the effectiveness of present method. • A singular ES-FEM is developed for dynamic brittle crack growth modeling. • Adaptive mesh refinement around a crack tip improves the accuracy of solutions. • The balance recovery method is utilized to minimize energy error during remeshing operations. • The effectiveness and accuracy of the method are verified by benchmark problems. [ABSTRACT FROM AUTHOR]

• A novel and effective computational approach based on polygonal XFEM for 2D cracks analysis is presented. • Cartesian transformation method integrated into polygonal XFEM for numerical integration over polygonal domains is derived. • Efficiency in computational time of the developed approach using Cartesian transformation is obtained. • Single and mixed-mode stress intensity factors for crack problems with complicated configurations are analyzed. • Crack propagation analysis of complex geometry is studied. The extended finite element method (XFEM) has become a powerful and effective technique for modeling fracture problems without remeshing. In this paper, we introduce a novel and effective computational approach that is based on polygonal XFEM (named as PolyXFEM) for the analysis of two-dimensional (2D) linear elastic fracture mechanics problems. The PolyXFEM is equipped with a new numerical integration technique that uses the concept of Cartesian transformation method (CTM) over polygonal domains. The underlying idea of the CTM is to transform a domain integral into a boundary integral and a one-dimensional integral. This is computationally more efficient compared to the two-level mapping integration commonly used on polygons. Furthermore, the PolyXFEM is effective in modeling crack problems due to the local enrichment based on the partition of unity method. Our numerical results show that improvements in accuracy are reached thanks to the higher-order of the polygonal shape functions of the PolyXFEM. In addition, efficiency in computational time is achieved because of the usage of the CTM integration scheme, which appears to be quite suitable for polygonal domains. To demonstrate the accuracy and performance of the developed PolyXFEM approach, several numerical examples for 2D linear elastic fracture problems are considered, in which static stress intensity factors and crack propagation are investigated and compared with reference solutions. The convergence and mesh independence of the PolyXFEM for crack analysis is also analyzed. [ABSTRACT FROM AUTHOR]

Abstract Glass structures are often used in industries utilising large structural topologies. These structures are typically manufactured by post-curing subcomponents together, using a chopped strand mat layer at the interface. To predict failure of these joints requires an accurate assessment of the material and fracture properties. In this paper two industrially manufactured top-hat stiffened panels are tested to determine the fracture behaviour at the component level. This highlights that the variability seen in fracture properties at coupon level is less evident in structural component response. Then a previously developed set of material properties is used to accurately model the structural response, crack initiation and debonding of the panels under four point bend using Finite Element Analysis which gives final failure at 6.2 kN and a 4.4% error compared to the experimental results which exhibits final failure at 5.94 kN. The specific fracture properties tested and R curve are shown to be critical in assessing crack initiation and propagation with considerable error, 14.5%, provided by data assumed from the literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper reports experimental results of the debonding propagation of bundled-fibers specimens subjected to a tensile stress wave. In addition, the paper also presents a dynamic debonding model for the problem on the basis of the cohesive zone model, and verifies the model by comparing the predicted debonding to the experimental data. The established numerical model is used to study the propagation mode of the debonding, and the result suggests that in this particular specimen design and loading condition, the debonding initiated in a mixed mode condition. However, the mode II quickly increased and dominated the mode I during an early debonding propagation up to certain extend where the mode mixity became constant. [Copyright &y& Elsevier]

Abstract: This paper presents the results of a finite element micromechanical simulation of the interaction between a matrix of voids and a crack for combinations of in-plane and out-of-plane constraint for an elastic–plastic material. Attention has been paid to the effects of out-of-plane constraint since previously this has rarely been investigated. It is known that in-plane and out-of-plane constraint have essentially the same influence on fracture and therefore a parameter should exist that quantifies their combined effect, although despite the efforts of researchers no unique measure of constraint has yet been found. In this paper it is argued that if the equivalent plastic strain upon fracture is used to rank the experimental data, a unique trend can be obtained. By using this trend, a new micromechanical fracture criterion is suggested for aluminium alloy 2024 that accounts for any level of in-plane and out-of-plane constraint. Finally, the findings are verified by comparison with three different sets of earlier experiments performed by the authors or extracted from the literature. [Copyright &y& Elsevier]

Abstract: Presented in this paper are the results pertaining to technical condition diagnostics, redesign, and analysis of its effects for a complex mechanical system of a polypropylene yarn twisting machine. Twelve twisting machines were installed on a polypropylene yarn production line. Due to design flaws and manufacturing errors, the winches were soon prone to failures and an unacceptable level of vibrations. Owing to insufficient structure rigidness, errors in design, manufacturing errors, and a high level of vibrations, the majority of twisting machines developed cracks in their foundation framework. FEM analysis was used with experimentally measured displacements in the crack zone to define stress distribution. Also shown in this paper is the method for measurement and analysis of the vibration signal during the winch run-up, with the aim to determine resonance zones and a condition analysis of the twisting machine framework. In order to make the winches fully operational, a redesign of the mechanical structure was performed. The level of vibration was measured again at the characteristic framework parts, and FEM analysis of the foundation framework was used to analyse the effects of the redesign. The vibration measurements and the results of FEM analysis proved that the redesign was successful, showing that the measures undertaken made this system fully operational again. [Copyright &y& Elsevier]

In the present paper 3D rate sensitive constitutive model for modeling of laminate composites is presented. The model is formulated within the framework of continuum mechanics based on the principles of irreversible thermodynamics. The matrix (polyester resin) is modeled by employing a 3D rate sensitive microplane model. For modeling of fibers (glass) a uni-axial constitutive law is used. The fibers are assumed to be uniformly smeared-out over the matrix. The formulation is based on the assumption of strain compatibility between matrix and fibers. Total stress tensor is additively decomposed into the contribution of matrix and fibers, respectively. To model de-lamination of fibers, the matrix is represented by periodically distributed initial imperfection over the pre-defined bands, which are parallel to fibers. Physically, this assumption accounts for the matrix-fiber interface in a smeared way. The input parameters of the model are defined by the mechanical properties of matrix and fibers (elastic properties, strength and fracture energy), the volume fraction of fibers and by their spatial orientation. The model is implemented into a 3D finite element code. To assure mesh objective results crack band method is employed. The model is first calibrated using a few basic test results. Subsequently, the model is validated with several numerical examples for specimens loaded in uni-axial tension, uni-axial compression and shear. Comparison between numerical and test results shows that the proposed model is able to predict the resistance and failure mode of complex fiber-reinforced composite for different orientation of fibers and different loading conditions with sufficient accuracy. Finally, based on the qualitative type of the finite element analysis, it is demonstrated that the strain rate dependency becomes more important when the angle between the fiber and load direction increases. [ABSTRACT FROM AUTHOR]

This paper presents a parallel generalized finite element method ( GFEM) that uses customized enrichment functions for applications where limited a priori knowledge about the solution is available. The procedure involves the parallel solution of local boundary value problems using boundary conditions from a coarse global problem. The local solutions are in turn used to enrich the global solution space using the partition of unity methodology. The parallel computation of local solutions can be implemented using a single pair of scatter-gather communications. Several numerical experiments demonstrate the high parallel efficiency of these computations. For problems requiring non-uniform mesh refinement and enrichment, load unbalance is addressed by defining a larger number of small local problems than the number of parallel processors and by sorting and solving the local problems based on estimates of their workload. A simple and effective estimate of the largest number of processors where load balance among processors is maintained is also proposed. Several three-dimensional fracture mechanics problems aiming at investigating the accuracy and parallel performance of the proposed GFEM are analyzed. [ABSTRACT FROM AUTHOR]

Abstract: As a volumetric heat source, YAG laser can penetrate through the glass, and has many advantages in cutting of glass with controlled fracture compared with CO2 laser cutting of glass. This work lays great emphasis on studying the technique of YAG laser cutting of multi-layer glasses. This paper indicates the experiments of YAG laser cutting of two-layer and four-layer soda-lime glasses with controlled fracture. Optical microscope photographs of the separation surface are obtained to examine the surface quality. The impact of laser power, scanning speed and laser beam size on the cutting quality is studied and the optimum processing parameters are presented in the paper. A theoretical model of a thermal laser shock method for separation of two-layer glasses is developed, and the fracture propagation mechanism is studied by examining the temperature and stress fields using finite element software ANSYS. In YAG laser cutting of multi-layer glasses, the temperature distribution is uniform across the thickness of the glass and the fracture propagates from the top and bottom surface to middle so that better separation surface quality can be acquired and multi-layer glasses can be cut simultaneously. [ABSTRACT FROM AUTHOR]

In the paper, the results of numerical failure analysis of plain concrete beams loaded by impact three-point bending load are presented and discussed. The theoretical framework for the numerical analysis is continuum mechanics and irreversible thermodynamics. The spatial discretization is performed by the finite element method using update Lagrange formulation. Green–Lagrange stain tensor is used as a strain measure. To account for cracking and damage of concrete, the beam is modeled by the rate sensitive microplane model with the use of the so-called co-rotational stress tensor. Damage and cracking phenomena are modeled within the concept of smeared cracks. To assure objectivity of the analysis with respect to the size of the finite elements, crack band method is used. The contact-impact analysis is based on the mechanical interaction between two bodies—concrete beam (master) and dropping hammer (slave) falling on the mid span of the beam. The contact constrains are satisfied by Lagrange multiplier method, which is adapted for the explicit time integration scheme. To investigate the influence of loading rate on the failure mode of the beam parametric study is carried out. The numerical results are evaluated, discussed and compared with test results known from the literature. It is shown that the beam resistance and failure mode strongly depend on loading rate. For lower loading rates beam fails in bending (mode-I fracture). However, with increasing loading rate there is a transition of the failure mechanism from bending to shear. The results are in good agreement with theoretical and experimental results known from the literature. [ABSTRACT FROM AUTHOR]

Over the past years, with increasing traffic volumes and higher wheel loads, fatigue damage in steel parts of typical orthotropic steel bridge decks has been experienced on heavily trafficked routes. A demand exists to find a durable system to increase the fatigue safety of orthotropic steel bridge decks. A solution might be to enhance the stiffness of the traditional orthotropic bridge deck by using a cement-based overlay. In this paper, an orthotropic steel bridge deck stiffened with a cement-based overlay is analyzed. The analysis is based on nonlinear fracture mechanics, and utilizes the finite-element method. The stiffness of the steel deck reinforced with an overlay depends highly on the composite action. The composite action is closely related to cracking of the overlay and interfacial cracking between the overlay and underlying steel plate (debonding). As an example, a real size structure, the Faro\ bridges located in Denmark, are analyzed. The steel box girders of the Faro\ bridges spans 80 m, and have a depth of 3.5 m, and a width of 19.5 m. The focus of the present study is the top part of the steel box girders, which is constructed as an orthotropic deck plate. Numerous factors can influence the cracking behavior of the cement-based overlay system. Both mechanical and environmental loading have to be considered, and effects such as shrinkage, temperature gradients, and traffic loading are taken into account. The performance of four overlay materials are investigated in terms of crack widths. Furthermore, the analysis shows that debonding is initiated for a certain crack width in the overlay. The load level where cracking and debonding is initiated depends on the stress-crack opening relationship of the material. [ABSTRACT FROM AUTHOR]

Abstract: Carbon nanotubes (CNT) possess remarkable mechanical, thermal and electrical properties, which combined with their low density and high aspect ratio, make them a very attractive candidate as reinforcing materials for the development of an entirely new class of composites. However, to determine CNTs mechanical properties in a direct experimental way is a challenging and not economical task, because of the technical difficulties and the costs involved in the manipulation of nanoscale objects. Moreover, there is still a lack of the fundamental knowledge regarding the strength and failure behaviour of carbon nanotubes. Due to nanoscale, most of the continuum based classical fracture mechanics are not really suitable to describe the failure evolution. Failure of nanotubes has been mainly investigated using molecular dynamics theory. In this paper, we present an innovative method for modelling the failure of carbon nanotubes under uniaxial tensile loading. CNT can be thought as structural systems, where the primary bond between two nearest-neighbouring atoms forms the axially loaded-bearing components member and the individual atom acts as joints of the related load-bearing members. A Finite Element Model, based on the molecular mechanics theory, is proposed in this paper in order to investigate the fracture progress in Zig-Zag and Armchair carbon nanotube with defects under uniaxial tensile stress. The novelty of the proposed approach lies in the use of nonlinear axial and torsional springs to model the local interaction and breakage of bonds of CNT atoms under axial loads. The complete load–displacement relationship of Force/Displacement curve for a (5,5) and a (9,0) nanotube up to the complete fracture was obtained. Further, with a continuum assumption, it was possible to define a Stress/Strain curve with ultimate strength and strain. The results show that the effect of chirality on the mechanical properties and failure mode of CNTs was quite significant and cannot be neglected. Moreover, the results are in good agreement with experimental data and classical molecular dynamics simulation validating, therefore, the proposed modelling approach. [Copyright &y& Elsevier]

A known factor that limits the performance of automotive front-end accessory serpentine belt drive is cracking of the elastomer located in the rib tip. In this paper, fracture experiments were conducted using single-edge notched tension (SENT) specimens to study the fracture behaviour of a belt rib compound. A finite-element modelling method utilizing singular elements for crack in rubber solid was proposed and implemented in both plane-stress and 3D solid models using ABAQUS. A newly developed neural-network-based model was used to represent a nonlinear elastic belt rib rubber compound. The crack finite-element model, along with the neural-network-based material model, was verified with analytical and experimental results. A global–local finite-element procedure was developed to evaluate the J-integral for mode-I through-the-thickness crack in V-ribbed belt rib. Effects of pre-crack length, pulley pre-load and backside pulley displacement were investigated. [ABSTRACT FROM AUTHOR]

The deformation and failure of spot-welded joints have been successfully modelled using a cohesive-zone model for fracture. This has been accomplished by implementing a user-defined, three-dimensional, cohesive-zone element within a commercial finite-element package. The model requires two material parameters for each mode of deformation. Results show that the material parameters from this type of approach are transferable for identical spot welds in different geometries where a single parameter (such as maximum stress) is not. The approach has been demonstrated using a model system consisting of spot-welded joints made from 5754 aluminium sheets. The techniques for determining the cohesive fracture parameters for both nugget fracture and nugget pullout are described in this paper. It has been demonstrated that once the appropriate cohesive parameters for a weld are determined, quantitative predictions can be developed for the strengths, deformations and failure mechanisms of different geometries with nominally identical welds. [ABSTRACT FROM AUTHOR]