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Abstract: Continuum damage mechanics (CDM) is used to describe the post-elastic behavior of low-basis-weight paper. The relevance of undertaking studies of the mechanical behavior of low-basis-weight paper is that it enables characterization, optimization and quality control. In accordance with a CDM theory, an internal variable is introduced that represent the degree to which the material has degraded in a continuum sense and details inherent in a damage evolution law contain information about the rupture mechanism. To account for long ranging micro-structural effects, because of the fiber structure in the paper material, a non-local formulation of the constitutive law is considered. Of particular interest is the fracture toughness of the material, i.e. the ability to resist further crack propagation, as it is often a good measure of flaw tolerance and durability in the context of paper. The constitutive model discussed is verified against tensile tests on rectangular paper specimens containing pre-fabricated cracks. Acoustic emission was used to study the damage evolution in paper specimens during tensile loading. An orthotropic material description has been utilized. The model is contrasted with a purely isotropic formulation. It seems that for the type of problem analyzed in this work, an orthotropic material description does not significantly improve the predictive capability as compared to an isotropic formulation. It is concluded that the model can be used to evaluate the influence of arbitrary defect geometries, defect size and loading conditions and can easily be incorporated into a finite element code. [Copyright &y& Elsevier]

Abstract: The mechanical behavior of fibrous networks is governed by complex multiple mechanisms. This study examines the effect of microstructure on the macroscopic deformation and fracture of two-dimensional random fiber networks and its practical implications for understanding the material failure in paper materials by using finite element models. Remote load is a pure mode I opening field, applied via a boundary layer. Characteristic networks, consisting of the union of solutions of several unique networks, are interpolated on a rectangular grid covering the whole problem domain. The interpolated solutions are interpreted as network-equivalent continuums representing the mechanical behavior, on average, for a specific set of structural properties. A regularization routine is included in a variational procedure in order to minimize potential energy in the body and produce continuous strains at cell borders in the grid. It is shown that using a classical continuum linear elastic fracture mechanics (LEFM) approach to describe macroscopic singular-dominated fields in fiber networks, can lead to erroneous results especially in networks having a low degree of bonds per fiber. The classical continuum description is too simple to capture the essential mechanical behavior for this class of material since a structural effect, that alters the displacement field, becomes pronounced. It is necessary to include a nonlocal theory to describe the mechanical behavior at a continuum level. By using an appropriate characteristic length in a nonlocal continuum formulation, strain energies, in the neighborhood of a dominant macroscopic singularity, are calculated that agree well with characteristic network models and hence produce fairly good agreements between the networks and the nonlocal continuum models. A key conclusion found is that, only for networks with a high degree of bonding, can the mechanical behavior around a macroscopic singularity be captured by the classical local continuum theory. In networks with a low degree of bonds per fiber, there are regions far away from the macroscopic singularity that have relatively higher magnitudes of strain energy than predicted by the classical theory. A relation between an internal length scale parameter, used in the nonlocal continuum model, and the structural properties of the network is approximated by a simple function. [Copyright &y& Elsevier]

The Strong Discontinuity Approach (SDA) is a popular method to incorporate cracks as displacement discontinuities into finite elements. In the first part of the paper, different SDA formulations (denoted as SOS, KOS and SKON) are assessed numerically based upon different error norms including a norm to evaluate the variational consistency of SDA elements. Results are compared with analytical solutions as well as with results from interface elements and the element erosion technique for cohesionless cracks. In the second part of the paper, a new method to improve the computational robustness of SDA analyses is proposed. In addition to using arc-length control to solve the nonlinear equation system, a sequential un- and reloading scheme is proposed with the crack state frozen during unloading to avoid, that more than one new crack segment is activated within an increment. The performance of the algorithm is demonstrated by numerical analyses of a tension test on a dog-bone shaped specimen by means of different variants of the SDA and, for comparison, also using interface elements. [ABSTRACT FROM AUTHOR]

• The finite element (FE) simulation of the hemispherical punch tests was performed for AA7075-O sheets in ABAQUS/Explicit using different time dependent criteria to predict the forming limit diagram at room temperature. • In order to understand the efficiency of the FE-based time dependent criteria to predict forming limit diagrams (FLDs), an analytical-based method, namely, Marciniak-Kuczynski (M-K) was tested. • It was observed that the experimental FLD can be reproduced using various time-dependent criteria in a relatively appropriate manner but with limitations. In this study, numerical simulations and experimental validations of the simulation of hemispherical punch tests for AA7075-O aluminum sheets with various sample widths are presented. It is convincingly believed in literature that a finite element (FE) based forming limit diagram (FLD) can be predicted very well using various time-dependent criteria. This matter has been investigated and securitized deeply and the FE-based FLD was predicted using three time-dependent criteria and compared with the experimental FLD. Results show that two of the three criteria could predict the relatively appropriate shape of the FLD while one of them has failed to match. Aside from using FE simulation to predict the FLD, an analytical method, namely, Marciniak-Kuczynski (M-K) was also used to make a better evaluation about the capability of the finite element method (FEM) to predict FLD. Among the FE-based FLDs, the one predicted using the Martinez-Donaire et al., 2014 was found to be close to the one predicted using the M-K method. Although, the main objective of this paper is to investigate the capability of the FEM to predict an FLD for AA7075-O aluminum sheets, the fracture behavior for each case was predicted using a unified fracture model. Several computer runs were executed to perform the tests and reproduce the experimental results. The aim of this study was to discuss the simulation of hemispherical punch tests and analyze the numerical results and compare them with the experimental and analytical methods. It was observed that the experimental FLD can be reproduced using various time-dependent criteria in a relatively appropriate manner but with limitations especially at the equibiaxial stress state. These limitations were scrutinized and discussed in detail by comparing the results with experimental and analytical calculations. [ABSTRACT FROM AUTHOR]

In this paper, a numerical analysis has been conducted to predict the fracture response of a novel type of fiber-reinforced concrete blocks, called "multi-functional fiber reinforced concretes" (MFRCs). In MFRCs, fibers have been coated with a shell. This will allow the structure to be used for multiple purposes, including concrete self-healing. This study is conducted utilizing phase-field fracture framework. The shell thickness and the ratio of fiber length to diameter are the geometrical parameters whose effects on the fracture resistance of the MFRCs have been analyzed. As choosing the right shell material is under investigation, in the next step of the study, in addition to the geometrical factors, different material mismatch cases for the critical energy release rate of the shell has been analyzed. Moreover, the application of two different fibers, polyester fiber and polypropylene fiber (with almost 10 times higher critical energy release rate), are looked into. All the structures undergo three loading conditions: tensile loading, compressive loading, and three-point bending. In order to judge what configuration performs best, the values of peak force and absorbed energy of each structure in each case study have been taken into consideration and compared with those of other structures. It was seen that the most favorable performance and configuration depend on the loading condition and also the material set. Under tension, MFRCs with the lowest fiber length to diameter ratio exhibit the highest peak force and absorbed energy in the case of polyester fiber. The same observation was made for all models and material sets under compressive loading. Under three-point bending loading condition, for the cases of polyester fiber, similar results were obtained as the lowest fiber length to diameter ratio showed the best mechanical response. Having said that, it must be mentioned that shell material had a dominant effect on the fracture response of the structure under this loading condition. Polypropylene fibers also managed to increase the peak forces in different loading conditions. • A novel multi-functional coated fiber-reinforced concrete (MFRC) is proposed. • Parametric study on fracture of MFRCs is conducted through phase-field framework. • For polyester fiber, lower lengths of fiber show higher toughness. • Polypropylene fiber increases peak forces while fail at lower displacement loads. • Less tough coating increases energy absorption under flexural loading. [ABSTRACT FROM AUTHOR]

Abstract: The stresses near a crack which has a fluid escaping through it are presented in this paper. The pressure and heat flux, due to the fluid acting on the crack walls, are imposed as boundary conditions in a new finite element tool which has been developed specifically for Leak-before-Break. This special tool uses the extended finite element method to include information about the problem on a sub element level. It is shown to be as accurate as standard finite element models which use very refined meshes, but having the added benefit of being much quicker to implement, and vastly reducing postprocessing. This means that leak rates can be investigated more efficiently. The model is thermo-elastic, and plasticity is accounted for by a correction to the crack opening displacement based on the R6 method. Both crack opening area and peak stresses are shown to decrease when the walls of the crack are hotter than the background plate temperature. The consequences of this for Leak-before-Break assessments are discussed in the paper. [Copyright &y& Elsevier]

Nonlinearities effects at the crack tip, due to the elastic-plastic material behavior, impact the crack growth rate and path. This paper is devoted to the study of the plastic zone evolution in the crack tip region. The methodology relies on coupling an elastic-plastic Finite Elements Method (FEM) model and experimental displacements measured by Digital Image Correlation (DIC). These latter are introduced as Dirichlet boundary conditions in the finite elements analysis. The considered FEM domain is constant, i.e. the same mesh with a centered crack is moved to each new crack tip position deduced from DIC. The new boundary conditions are updated and the residual stresses and plastic strains of the former computation are interpolated and actualized on the mesh shifted to the new crack tip position in order to incorporate them in the numerical model. The coupling method allowed applying experimental boundary conditions in order to be as close as possible to real experimental conditions and to observe the plasticity evolution from small to large scale yielding conditions. A fatigue test was conducted to validate the proposed approach. The identification residues are proved to be lower than those obtained with an experimental displacements projection onto Williams' series basis, which is a method commonly used with DIC. The coupling results present an attractive similarity with Irwin's model regardless of the crack length. Thus, the definition of the mask needed for the displacements fields projection on Williams' model can be deduced with a reliable estimate of Irwin's plastic radius. [ABSTRACT FROM AUTHOR]

Abstract: This paper explores the specimen-dependence of the resistance (R-) curve for fracture of materials showing a pronounced R-curve effect. Using a cohesive zone framework, this paper demonstrates how to effectively predict the R-curve for a specimen type whose deformation is shear-dominated (compact tension, CT) from the R-curve of a specimen type whose deformation is bending-dominated (double cantilever beam, DCB). The mathematical relationships between crack extension and crack opening displacements for both CT and DCB specimens are first derived and related to a tri-linear cohesive law. Experimental tests for intralaminar fracture of CFRP are carried out and analysed. Using, as input, the experimental results from the DCB specimen, the cohesive law is shown analytically and using Finite Element (FE) to reproduce accurately the R-curve for the DCB and also to predict accurately the R-curve for the CT specimens. [Copyright &y& Elsevier]

Abstract This paper introduces a shell based finite element (FE) model for predicting the impact response and dominant failure mechanisms of fiber reinforced polymer matrix composites subject to low-velocity impact. The model utilizes Enhanced Schapery Theory (EST) for capturing the matrix non-linearity due to micro cracking as well as macroscopic intra-lamina failure, that is, matrix cracking and fiber rupture in the 1–2 failure plane of a lamina. Discrete cohesive elements (DCZM) are utilized for capturing the inter-lamina failure initiation and propagation. The intra- and inter-lamina damage and failure models are implemented as user subroutines in the commercial finite element solver, ABAQUS Explicit. The model is compared against low-velocity impact experimental data. High fidelity non-destructive inspection (NDI) methods are used to quantify the impact damage for a detailed comparison to the model predictions. The modeling technique shows excellent agreement with experimental results, both for impact response and damage evolution. [ABSTRACT FROM AUTHOR]

Abstract: Several published papers deal with the possibility of replacing a damage finite element model by a combination of cohesive zones and finite elements. The focus of the paper is to show under which conditions this change of model can be done in an energy-wise manner. The objective is to build a cohesive model based on a known damage model, without making any assumption on the shape of the cohesive law. The method is characterized, on the one hand, by the use of a well-defined thermodynamic framework for the cohesive model and, on the other hand, by the idea that the main quantity which must be maintained through the change of model is the energy dissipated by the structure. An analysis of the stability criteria enables us to determine the domains of validity of the different models. Thus, we show that it is consistent to derive the cohesive law from a given nonlocal damage model because the occurrence of a discontinuity can be viewed as an alternative way to limit localization. The method is illustrated on one-dimensional examples and a numerical resolution method for the problem with a cohesive zone is presented. [Copyright &y& Elsevier]

This paper presents a general formulation for the analysis of reinforced concrete frames. The model has been developed within the framework of lumped damage mechanics. This is a theory based on the methods of continuum damage mechanics, fracture mechanics and the concept of plastic hinge. The paper also describes the numerical implementation of the model in the finite element programs. The model is evaluated by the numerical simulation of three tests reported in the literature. Two of them deal with a column subjected to variable axial loads and biaxial flexure. The third is a two-story three-dimensional frame subjected to earthquake loadings outside the principal directions of the frame. [Copyright &y& Elsevier]

For several technical applications the dynamic aspect in fracture mechanics cannot be neglected. When the reliability of components with macroscopic cracks has to be assessed, the consideration of dynamic effects may lead to much higher stress intensity factors than under static conditions. In this paper three different methods to calculate the dynamic stress intensity factor for the mode-I loading of stationary cracks are compared. Based on two- and three-dimensional finite element simulations, the dynamic stress intensity factor is computed with the dynamic J-integral, the modified crack closure integral and the displacement interpretation method. The theoretical fundamentals of all three methods are summarized in the paper and the numerical implementation is explained briefly. Results for different models are shown and compared to findings in the literature. [Copyright &y& Elsevier]

This paper presents a new adaptive multiscale homogenization scheme for the simulation of damage and fracture in concrete structures. A two-scale homogenization method, coupling meso-scale discrete particle models to macro-scale finite element models, is formulated into an adaptive framework. A continuum multiaxial failure criterion for concrete is calibrated on the basis of fine-scale simulations, and it serves as the adaptive criterion in the multiscale framework. Thus, in this approach, simulations start without assigning any material Representative Volume Element (RVE) to the macro-scale finite elements. The finite elements that meet the adaptive criterion and must be entered into the multiscale homogenization framework are detected on the fly. This leads to a substantial reduction of the computational cost especially for loading conditions leading to damage localization in which only a small portion of the FE mesh is enriched with the homogenized RVE. Several numerical simulations are carried out to investigate the capability of the developed adaptive homogenization method. In addition, a detailed study on the computational cost is performed. [ABSTRACT FROM AUTHOR]

Generalised functions have been widely adopted in structural mechanics to treat singularities of beam-like structures. However due to the curved geometry, that couples axial and transversal displacements, their use has never been explored for curved beams. In this paper the capability of distributions of leading to closed form exact solutions for multi-cracked circular arch is shown. The exact closed-form solution of a circular Euler arch in presence of any number of discontinuities due to concentrated damage and subjected to an arbitrary distribution of static loads is obtained. Damage, under the form of concentrated cracks, has been modeled through the widely adopted and validated equivalent elastic hinge concept and has been introduced in the governing differential equations by making use of Dirac's delta functions. The resulting nontrivial generalised six order differential equations have been derived and solved in closed form. Independently of the number of along arch concentrated cracks, the solution is expressed as a function of six integration constants only in which the damage positions and intensities are given data appearing explicitly in the solution expression. This latter aspect constitutes a fundamental aid towards the resolution of the static damage inverse identification problem. The results have been validated through some comparisons with finite element numerical simulations: examples referred to multi-cracked Euler arches with different boundary conditions, damage and load scenarios are presented. [ABSTRACT FROM AUTHOR]

• The XFEM is implemented to study dynamic crack propagation under thermal impact. • Novel tip enrichment functions, derived based on the asymptotic fields of a dynamically growing crack are implemented. • The effect of the dissipation coefficient as well as the thermal shock magnitude on the crack propagation path is investigated. This paper addresses the dynamic crack growth in an isotropic media subjected to a non-classical thermal shock by implementing the Green-Naghdi (GN) generalized thermoelasticity theory in the eXtended Finite Element Method (XFEM). To satisfy the crack tip singularity for modeling dynamic crack growth via XFEM, proper enrichment functions for field variables are needed, which are extracted from the asymptotic fields for a dynamically growing crack in a thermoelastic media. These near tip fields of a dynamically moving crack are also used in the formulations of the maximum circumferential stress criterion and the equivalent stress intensity factor. Finally, numerical examples of the dynamic crack propagation under thermal shock are given out, and the effect of the dissipation coefficient in the GN model and the thermal shock amplitude on the crack growth path is studied in detail. In addition, the crack propagation under GN thermal shock is compared with that under classic thermal shock. The main difference between them is discussed in a numerical example. [ABSTRACT FROM AUTHOR]

This paper provides closed-form expressions for the process zone lengths and load-displacement responses of cohesive zone modeling, for the popular mode I double cantilever beam (DCB) test, the mode II end notched flexure (ENF) test and the mixed-mode I/II bending (MMB) test of composite materials. By incorporating traction-separation laws that consist of only one quasi-brittle softening segment, the problems are formulated and analytically solved for homogenous material or mid-plane symmetric laminates within the framework of classical lamination theory (CLT). The solutions of the MMB test are obtained by the superposition method. Having been known as depending on the mode mixity, the material and interfacial fracture properties, the process zone length is found as a system parameter that is also influenced by the specimen geometry, including the thickness and the crack length, especially for mode II. Based on the parametric studies and the comparison against finite element (FE) simulations, suggestions for estimating the process zone length are provided. [ABSTRACT FROM AUTHOR]

Cracks in kerogen-rich shales and other brittle rock-like materials have a tremendous impact on their elastic properties and strength. In this paper, we investigate the effective mechanical properties of shale plates with pre-existing cracks. We employ the extended finite element method (XFEM) to investigate a pre-cracked medium with an elastic, isotropic and brittle shale matrix. We show how the mechanical properties of the orthotropic shale plates are dependent on the crack density and the standard deviation of crack angles. Both the Young's modulus and the Poisson's ratio of the cracked media exhibit a linear dependence on the standard deviation of crack angles, in contrast to the nonlinear dependence of the strength on the angle deviation. Finally, we propose mechanical models to capture the relationship between the mechanical properties and the distribution characteristics of pre-existing cracks in shales. These phenomenological models could be applied to estimate the fracking behavior of shales in engineering practice. [ABSTRACT FROM AUTHOR]

A novel non-local lattice particle method for three-dimensional elasticity and fracture simulation of isotropic solids is proposed in this paper. First, the basic concept and detailed derivation of the proposed model are given. Three cubic lattice packing are investigated using the proposed model and simulation results are compared with classical finite element method solutions. The performance of these lattice structures are assessed using several benchmarks, for both deformation and brittle fracture problems. From the simulation results, good agreements with both analytical solution and experimental data are observed. Conclusions and future work are drawn based on this study. [ABSTRACT FROM AUTHOR]

The Tapered Double Cantilever Beam (TDCB) is the common specimen to study self-healing thermosetting polymers. While this geometry allows characterising the mode I fracture toughness without taking into account the crack length, the experiments show an important dispersion and unstable behaviour that must be taken into account to obtain accurate results. In this paper, finite element simulations have been used to understand the experimental behaviour. Static simulations with a stationary crack give the local stresses and the stress intensity factors at the crack tip when the TDCB is under load. In addition, the eXtended Finite Element Method (XFEM) has been used to make quasi-static crack propagation simulations. The results indicate that the crack tip has a curved profile during the propagation, advancing more at the edges than at the centre. The crack propagation begins when the applied load reaches a critical value. The unstable crack propagation noted in the experiments can be reproduced by introducing an unstable behaviour in the simulations. Finally, the sensitivity of the critical load has been studied as a function of the friction between pin and hole, tolerance of geometrical dimensions, and cracks out of the symmetric plane. The results can partially explain the dispersion of the experimental data. [ABSTRACT FROM AUTHOR]

This paper extends a semi-analytical technique, the so-called scaled boundary finite element method (SBFEM), to analyze fracture behaviors of piezoelectric materials and piezoelectric composites under thermal loading. In this method, only the boundary is discretized leading to a reduction of the spatial dimension by one. The temperature field in the domain is obtained using the SBFEM and expressed as a series of power functions of the radial coordinate. The resulting stress and electric displacement distribution along the radial direction is represented analytically. This permits the generalized stress and electric displacement intensity factors to be directly evaluated from the solution by following standard stress recovery procedures in the finite element method (FEM). Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

Recent experiments showed that the Lode parameter, which distinguishes between axisymmetric and shear dominated stress states, has a profound effect on material ductility, especially at low stress triaxiality (Bao and Wierzbicki, 2004; Barsoum and Faleskog, 2007a). Consequently, the theoretical framework for void growth and coalescence is currently being revisited, which often involves performing representative volume element (RVE) calculations. The present study investigates an RVE composed of a cubic unit cell containing a spherical void at its center. The void cell is subjected to a triaxial stress state with Σ 11 / Σ 22 = ρ 11 , Σ 33 / Σ 22 = ρ 33 , plus an additional shear stress component Σ 12 / Σ 22 = ρ 12 . In the coordinate axes aligned with the edges of the cubic void cell, x i ( i = 1 , 2 , 3 ), the non-dimensional stress ratios ρ 11 , ρ 33 , and ρ 12 can be fully characterized by 3 parameters: the stress triaxiality, T , Lode parameter, L , and shear ratio, S . The aim of this paper is to provide an effective method to keep T , L , and S values constant in the entire course of the loading. The effectiveness of the proposed method is validated through several examples covering a wide range of T , L , and S values; the calculations are performed by using the general purpose finite element software ABAQUS. [ABSTRACT FROM AUTHOR]

Abstract: Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems. [Copyright &y& Elsevier]

Abstract: Magneto-electro-elastic (MEE) materials usually consist of piezoelectric (PE) and piezomagnetic (PM) phases. Between different constituent phases, there exist lots of interfaces with discontinuous MEE properties. Complex interface distribution brings a great difficulty to the fracture analysis of MEE materials since the present fracture mechanics methods can hardly solve the fracture parameters efficiently of a crack surrounded by complex interfaces. This paper develops a new domain formulation of the interaction integral for the computation of the fracture parameters including stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF) for linear MEE materials. The formulation derived here does not involve any derivatives of material properties and moreover, it can be proved that an arbitrary interface in the integral domain does not affect the validity and the value of the interaction integral. Namely, the interaction integral is domain-independent for material interfaces and thus, its application does not require material parameters to be continuous. Due to this advantage, the interaction integral becomes an effective approach for extracting the fracture parameters of MEE materials with complex interfaces. Combined with the extended finite element method (XFEM), the interaction integral is employed to solve several representative problems to verify its accuracy and domain-independence. Good results show the effectiveness of the present method in the fracture analysis of MEE materials with continuous and discontinuous properties. Finally, the particulate MEE composites composed of PE and PM phases are considered and four schemes of different property-homogenization level are proposed for comparing their effectiveness. [Copyright &y& Elsevier]

The peridynamic stress formula proposed by Lehoucq and Silling (2008) is cumbersome to be implemented in numerical computations. In this paper, we show that the peridynamic stress tensor has the exact mathematical expression as that of the first Piola–Kirchhoff static Virial stress originated from the Irving–Kirkwood–Noll formalism (Irving and Kirkwood, 1905; Noll, 1955) through the Hardy–Murdoch procedure (Hardy, 1982; Murdoch, 1983), which offers a simple and clear expression for numerical calculations of peridynamic stress. Several numerical verifications have been carried out to validate the accuracy of the proposed peridynamic stress formula in predicting the stress states in the vicinity of the crack tip and other sources of stress concentration. By evaluating the peridynamic stress in the prototype microelastic brittle (PMB) material model of bond-based peridynamics, it is found that the PMB material model may exhibit nonlinear constitutive behaviors at large deformations. The stress fields calculated through the proposed peridynamic stress formula show good agreements with these calculated by using finite element methods, analytical solutions, as well as experimental data, demonstrating the merit of the peridynamic stress formula in predicting stress states for material failure problems. [ABSTRACT FROM AUTHOR]

Loaded materials constrained by imperfect boundary can be found in many engineering scenarios, including blanking process, contact pressure sensor and soil/rock foundation subjected to underground mining. This paper examines the surface loading problem of a multilayered or functionally graded material (FGM) resting on an imperfect rigid smooth base weakened by a circular opening. The surface loading is axisymmetric and coaxial with the circular opening. This mixed boundary value problem is analogous to a Mode-I penny-shaped crack in multilayered elastic medium. With the aid of the GKS-based method for N-layered elasticity, the problem is formulated as a system of dual integral equations and then reduced to a Fredholm integral equation of the second kind. Solutions of the SIF, COD and full elastic field are expressed in terms of the solution of the integral equation. Numerical results obtained from the present solutions are compared with the those from finite element method. Using the new solutions, numerical studies are also conducted for four examples, including a homogenous layer, a multilayered material, a material with FGM coating and an asphalt pavement structure with FGM properties. These numerical results demonstrate that (1) a small size of surface loading can result in high SIF value at the crack tip; (2) placing the hard layer as the top surface is most effective for reducing ground settlement; (3) the gradation in Poisson's ratio can have non-negligible effect on the SIF for thin FGM coating; (4) effect of the circular opening to the ground settlement can be significant if its radius is comparable to the total thickness of the upper layers. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the deformation and failure mechanisms of wood at the ultrastructural scale. At this level, wood is composed of a periodic alternation of amorphous and crystalline cellulose fractions, embedded in a soft hemicellulose-lignin matrix. The mechanical response of wood is calculated under tensile loading conditions by means of the computational homogenisation of a representative volume element (RVE) of material. Three potential mechanisms of failure are suggested: axial straining of the crystalline fraction of cellulose, accumulation of plastic strain in the amorphous portion of cellulose and tensile rupture in the hemicellulose-lignin matrix due to cellulose fibres separation. In order to validate the present multi-scale framework, we compare our numerical predictions for the reorientation of cellulose fibres with experimental data, finding a good agreement for a wide range of strains. Furthermore, we assess successfully our numerical predictions for ultimate strains at the instant of failure when compared to experimental values. Numerical simulations show that our model is able to provide new clues into the understanding of how trees and plants optimise their microstructure in order to develop larger strains without apparent damage. A remarkable prediction by our model suggests that the extensibility of the material is maximised for initial microfibril angles (MFA) between 50° and 55°, a range of values found typically in branches of trees, in which the extensibility is an essential requirement. These findings are likely to shed more light into the dissipative mechanisms of wood and natural materials, which are still not well-understood at present. [Copyright &y& Elsevier]

Abstract: Piezoelectric materials and structures contain more or less electromechanical interfaces in engineering applications. It is difficult to obtain the fracture parameters efficiently of the piezoelectric materials with complex interfaces. This paper presents a domain-independent interaction integral for material nonhomogeneity and discontinuity which can be used for solving the stress intensity factors (SIFs) and the electric displacement intensity factor (EDIF) of piezoelectric materials with complex interfaces efficiently. The interaction integral is based on the J-integral by superimposition of two admissible states and the present formulation does not involve any derivatives of mechanical and electric properties. Moreover, it is proved that the interface in the integral domain does not affect the value of the interaction integral and thus, the present method does not require electromechanical parameters of piezoelectric materials to be continuous. The interaction integral method combined with the extended finite element method (XFEM) is used to investigate the influences of material continuity on the SIF and the EDIF and the results show that the material parameters and their first-order derivatives affect both the SIF and the EDIF greatly, while the higher-order derivatives affect both of them slightly. [Copyright &y& Elsevier]

Abstract: In this paper, the three-dimensional adaptive finite element modeling is presented for cohesive fracture analysis of non-planer crack growth. The technique is performed based on the Zienkiewicz–Zhu error estimator by employing the modified superconvergent patch recovery procedure for the stress recovery. The Espinosa–Zavattieri bilinear constitutive equation is used to describe the cohesive tractions and displacement jumps. The 3D cohesive fracture element is employed to simulate the crack growth in a non-planar curved pattern. The crack growth criterion is proposed in terms of the principal stress and its direction. Finally, several numerical examples are analyzed to demonstrate the validity and capability of proposed computational algorithm. The predicted crack growth simulation and corresponding load-displacement curves are compared with the experimental and other numerical results reported in literature. [Copyright &y& Elsevier]

Abstract: In this paper, a new method for level set update is proposed, in the context of crack propagation modeling with the extended finite element method (X-FEM) and level sets. Compared with the existing methods, such as the resolution of the Hamilton–Jacobi equations, this new method is much simpler because it does not required complex manipulations of the level sets. This method, called the “projection” method, uses both a classical discretization of the surface of the crack (segments for 2d cracks and triangles for 3d cracks) and a level set representation of the crack. This discretization is updated with respect to the position of the new crack front. Then the level sets are re-computed using the true distance to the new crack, by an orthogonal projection of each node of the structure onto the new crack surface. Then, numerical illustrations are given on 2d and 3d academic examples. Finally, three illustrations are given on 3d industrial applications. [Copyright &y& Elsevier]

Abstract: Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary crack lengths and material combinations. In this paper the stress intensity factors of an edge interface crack in a bonded strip are considered under tension with varying the crack length and material combinations systematically. Then, the limiting solutions are provided for an edge interface crack in a bonded semi-infinite plate under arbitrary material combinations. In order to calculate the stress intensity factors accurately, exact solutions in an infinite bonded plate are also considered to produce proportional singular stress fields in the analysis of FEM by superposing specific tensile and shear stresses at infinity. The details of this new numerical solution are described with clarifying the effect of the element size on the stress intensity factor. It is found that for the edge interface crack the normalized stress intensity factors are not always finite depending upon Dunders’ parameters. This behavior can be explained from the condition of the singular stress at the end of bonded strip. Convenient formulas are also given by fitting the computed results. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to propose a novel methodology for determining dynamic fracture toughness (DFT) of materials under mixed mode I/II impact loading. Previous experimental investigations on mixed mode fracture have been largely limited to qusi-static conditions, due to difficulties in the generation of mixed mode dynamic loading and the precise control of mode mixity at crack tip, in absence of sophisticated experimental techniques. In this study, a hybrid experimental–numerical approach is employed to measure mixed mode DFT of 40Cr high strength steel, with the aid of the split Hopkinson tension bar (SHTB) apparatus and finite element analysis (FEA). A fixture device and a series of tensile specimens with an inclined center crack are designed for the tests to generate the components of mode I and mode II dynamic stress intensity factors (DSIF). Through the change of the crack inclination angle β (=90°, 60°, 45°, and 30°), the K II/K I ratio is successfully controlled in the range from 0 to 1.14. A mixed mode I/II dynamic fracture plane, which can also exhibit the information of crack inclination angle and loading rate at the same time, is obtained based on the experimental results. A safety zone is determined in this plane according to the characteristic line. Through observation of the fracture surfaces, different fracture mechanisms are found for pure mode I and mixed mode fractures. [Copyright &y& Elsevier]

Abstract: A three-dimensional extension of a previously published two-dimensional cracked finite element [Potirniche, G.P., Hearndon, J., Daniewicz, S.R., Parker, D., Cuevas, P., Wang, P.T., Horstemeyer, M.F., 2008. A two-dimensional damaged finite element for fracture applications. Engineering Fracture Mechanics 17(13), 3895–3908] is presented in this paper. The new element has an embedded edge crack, and was developed to model damage in three-dimensional structures using the finite element method. The element simulates the presence of a crack without physically inserting it in the three-dimensional finite element mesh. The method involves the derivation of a modified stiffness matrix that accounts for the change in the element flexibility due to the crack presence. The cracked element was analytically formulated and implemented in the finite element code ABAQUS Standard as a User-defined Element (UEL) subroutine. Tests of various cracked beam configurations were used to estimate the accuracy of the element by comparing two models: one with a UEL and another with an embedded edge crack. Beam deflections and natural frequencies were analyzed and compared for the two models. The results indicate that the new element has a good potential in modeling cracks in three-dimensional parts. Moreover, the method using this UEL computes the global response of damaged structures, in which cracks can be placed at various locations and in an unlimited number. [Copyright &y& Elsevier]

Abstract: In this work, we have assessed the results of the local and nonlocal versions of Rousselier’s damage model, which have been used here for simulation of ductile crack growth. There are several issues regarding the accuracy of the results which has been addressed in this paper, e.g., accuracy in simulation of crack path, extent and width of the damaged region, fracture resistance behaviour in situations such as symmetric vs. non-symmetric boundary-value problems, mixed-mode loading vs. mode-I loading of the crack-tip, etc. It was also observed that the shape and orientation of the elements at the crack-tip, in addition to their size, influence the results of the local damage model. In this work, it was shown that the above issues can be resolved through the use of nonlocal damage models. The predictions of the nonlocal model are also consistent with the experimental observations unlike its local counterpart. Several examples were presented, where the results as obtained by both the local and nonlocal models were compared. From this experience, it is recommended that the local damage models should not be used blindly by the analysts for all kinds of mesh design, loading, boundary conditions, etc. [Copyright &y& Elsevier]

Abstract: In this paper, we established a strain-gradient damage model based on microcrack analysis for brittle materials. In order to construct a damage-evolution law including the strain-gradient effect, we proposed a resistance curve for microcrack growth before damage localization. By introducing this resistance curve into the strain-gradient constitutive law established in the first part of this work (), we obtained an energy potential that is capable to describe the evolution of damage during the loading. This damage model was furthermore implemented into a finite element code. By using this numerical tool, we carried out detailed numerical simulations on different specimens in order to assess the fracture process in brittle materials. The numerical results were compared with previous experimental results. From these studies, we can conclude that the strain gradient plays an important role in predicting fractures due to singular or non-singular stress concentrations and in assessing the size effect observed in experimental studies. Moreover, the self-regularization characteristic of the present damage model makes the numerical simulations insensitive to finite-element meshing. We believe that it can be utilized in fracture predictions for brittle or quasi-brittle materials in engineering applications. [Copyright &y& Elsevier]

Abstract: Fracture in heterogeneous media is still an open topic in the research community. One of the main reasons is the fact that cracks may occur in widely different length scales. While microcracks can be satisfactorily modeled by a loss in the tangent moduli tensor without considering the microcracks explicitly, such as in continuum damage models, macrocracks cannot be accurately modeled unless a discontinuity is explicitly considered. This is especially true in wave problems, since reflection or transmission of the waves is greatly affected by the presence of a discontinuity. Furthermore, the (scale) transition of microcracks into macrocracks is a key mechanism that must be considered in order to accurately model fracture in heterogeneous materials. This paper presents a two-way coupled multiscale approach for modeling fracture in heterogeneous viscoelastic media and proposes a scheme to account for the transition of microcracks into macrocracks. The model has been implemented into a finite element code and numerical results are shown for demonstration purposes. [Copyright &y& Elsevier]

Abstract: In this paper, an energy parameter based on the concept of the M-integral is proposed for describing the fracture behavior of a multi-cracked solid subjected to nonconservative and nonuniform crack surface tractions. By using the M-integral with a suitably chosen closed contour, one can evaluate the ‘surface creation energy’ (SCE) required for creation of the stressed cracks. Also, it is demonstrated that the property of path-independence holds even under the action of crack surface tractions. Therefore, the singular stress field in the near-tip areas is not directly involved in the calculation so that a complicated finite element model around the crack tips is not required in evaluation of the M-integral. [Copyright &y& Elsevier]

Abstract: The behavior of concrete structures is strongly influenced by the loading rate. Compared to quasi-static loading concrete loaded by impact loading acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia forces activated. Both influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of the crack propagation of the concrete compact tension specimen. The rate sensitive microplane model is used as a constitutive law for concrete. The strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. The results of the study show that the fracture of the specimen strongly depends on the loading rate. For relatively low loading rates there is a single crack due to the mode-I fracture. However, with the increase of loading rate crack branching is observed. Up to certain threshold (critical) loading rate the maximal crack velocity increases with increase of loading rate, however, for higher loading rates maximal velocity of the crack propagation becomes independent of the loading rate. The critical crack velocity at the onset of crack branching is found to be approximately 500m/s. [Copyright &y& Elsevier]

Abstract: A three dimensional (3D) hybrid method combining the classical finite element (FE) method with the semi-analytical finite element (SAFE) technique is developed. This hybrid method is employed to study the interaction of guided waves with non-axisymmetric damages in cylinders. The near field surrounding the damage is analysed with the 3D FE method. The solution is expanded into sums of guided modes on both inlet and outlet cross-sections. Such eigenmode expansions enable separation into ingoing and outgoing waves, i.e., incident, reflected and transmitted waves. Using the SAFE method, elastic guided modes are then computed at the aforementioned cross-sections thus reducing the analysis to two dimensions (2D). The amplitudes of the incident modes are imposed, whereas those of the scattered modes are determined by solving the global system of the 3D hybrid FE-SAFE model. In this paper, a formula is proposed for the calculation of eigenforces and modal power flows from eigendisplacements and SAFE matrices. This has the advantage of simplifying the post-process of load eigenvectors in hybrid FE-SAFE methods. Results obtained for a vertical free-end cylinder are in good agreement with those published in the literature. Moreover, first results of the interaction of the fundamental compressional, flexural and torsional Pochhammer–Chree modes with non-axisymmetric vertical cracks are obtained and discussed. Then, the interactions of the fundamental compressional mode with oblique free-ends and cracks are briefly addressed. The power balance is shown to be satisfied with a good accuracy. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes an experimental and numerical investigation on the fracture behaviour of a cast AlSi9MgMn aluminium alloy. In the experiments, a modified Arcan test set-up was used to study mixed-mode fracture. During testing, the tension load and the displacement of the actuator of the test machine were recorded, simultaneously as a high-resolution digital camera was used to record a speckle-patterned surface of the specimen. The recorded images were post-processed using an in-house digital image correlation (DIC) software to obtain information of the displacement and strain fields in the specimen during the test. In addition, some newly implemented features in the DIC software allowed us to detect and follow the crack propagation in the material. The numerical calculations were carried out with a user-defined material model implemented in an explicit finite element code. In the model, the material behaviour is described by the classical J 2 flow theory, while fracture was modelled by the Cockcroft–Latham criterion, assuming the fracture parameter to follow a modified weakest-link Weibull distribution. With the proposed probabilistic fracture modelling approach, the fracture parameter can be introduced as a random variable in the finite element simulations. Crack propagation was modelled by element erosion, and a non-local damage formulation was used to reduce mesh-size sensitivity. To reveal the effect of mesh density and meshing technique on the force–displacement curves and the crack propagation, several different meshes were used in the numerical simulations of the modified Arcan tests. The numerical results were finally compared to the experimental data and the agreement between the measured and predicted response was evaluated. [ABSTRACT FROM AUTHOR]

Abstract: In an attempt to simulate non-uniform coating delamination, the elasto-static problem of a penny shaped axisymmetric crack embedded in a functionally graded coating bonded to a homogeneous substrate subjected to crack surface tractions is considered. The coating’s material gradient is parallel to the axisymmetric direction and is orthogonal to the crack plane. The graded coating is modeled as a non-homogeneous medium with an isotropic constitutive law. Using Hankel transform, the governing equations are converted into coupled singular integral equations, which are solved numerically to yield the crack tip stress intensity factors. The Finite Element Method was additionally used to model the crack problem. The main objective of this paper is to study the influence of the material non-homogeneity and the crack position on the stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings. [Copyright &y& Elsevier]

Abstract: A 2D X-FEM/LATIN numerical model (eXtended Finite Element Method/Large Time Increment method) is proposed in this paper for the analysis of fretting fatigue problems and the simulation of the crack propagation under such loadings. The half-analytical two-body contact analysis allows to capture accurately the pressure and the cyclic tractions exerted at the interface that induce non-proportional multi-axial loading. These distributions are then used as input data for determining critical location for crack initiation and crack inclination based on Dang Van’s criterion. The frictional contact conditions of the fretting fatigue cracks have an important impact on the crack behaviour. In this respect, contact with friction between the crack faces is finely modeled within the X-FEM frame. The obtained results are compared and validated with a half-analytical reference model. The numerical simulations reveal the robustness and the efficiency of the proposed approach for a wide range of fretting loadings and friction coefficients values along crack faces. The crack growth directions are then predicted accurately based on the use of criteria adapted to multi-axial non-proportional fatigue. Four cases dealing with crack propagation are then presented. It is shown how the crack length, the tangential loading modify the crack path during the propagation process. [Copyright &y& Elsevier]

Abstract: This paper treats evolution of ply cracks in multidirectional composite laminates subjected to a quasi-static tensile load in the longitudinal direction. Starting with pre-existing ply cracks in off-axis plies, the formation of additional cracks is analyzed by an energy-based approach. A critical laminate energy parameter associated with formation of these cracks is defined and is evaluated using experimental data for a reference cross-ply laminate. The modeling approach requires crack surface displacements, which are calculated by a three-dimensional finite element (3-D FE) analysis performed on a suitable representative volume of the given cracked laminate. The model predictions agree well with experimental data for laminates. A parametric study is conducted to evaluate effects of ply thickness and ply stacking sequence on damage evolution in laminates. [Copyright &y& Elsevier]

Abstract: A model for stress-induced phase transformation surrounding the crack tip during mode III fracture of shape memory alloys (SMAs) is introduced. Considering a state of small-scale yielding and J2 plasticity (loading only), the shape and size of the martensite (M), the austenite (A) and the transformation zone are fully determined. For a fixed crack length, the zones of constant strain around the crack tip develop as circles. The width of the transformation zone and the martensite both depend linearly on the crack length. Moreover, the crack tip is surrounded by martensite under plastic deformation. The theoretical model is then extended to examine the mode III fracture behavior of Nickel–Titanium (Nitinol), and these results are compared to FEM analysis of a edge crack torsion (ECT) test for an isotropic material. The size of stress-induced martensite zone in the FEM analysis is underestimated by about 50% from the theoretical model, due largely to the difference in the computed and theoretical stress–strain relation. However, the model and simulation show remarkable agreement on the size of the transformation zone (error<5%), which dominates the region surrounding the crack tip. In addition, the model predictions accurately match the FEM analysis in determining the radii circles of constant strain in the vicinity of the crack tip, and the shape and size of the plastically deformed martensite zone. The results presented in this paper provide a first step to better understand the mechanics of fracture in shape memory alloys under mode III loading. [Copyright &y& Elsevier]

Abstract: This paper describes studies of the near tip fields and the effects on void growth rates for a steadily advancing crack through a ductile metal in the presence of hydrogen, under plane-strain and quasi-static conditions. The computational model determines directly the deformation history of a steadily propagating crack without the need for a priori (transient) analysis that considers blunting of the pre-existing stationary crack and subsequent growth through the associated initial plastic zone. The present approach enables straightforward investigation over a range of geometric constraint configurations encountered in test specimens and structural components by application of a far field loading. The ductile crack propagation simulated in these studies represents that observed in a high-solubility model material, where the diffusion rate can sustain equilibrium of the hydrogen concentration ahead of the steadily propagating crack tip. The constitutive model accounts for the influence of hydrogen on the elastic–plastic regimes of material response at the continuum level, e.g. hydrogen-induced material softening. The model reflects the amount of hydrogen in the material under stress and the intensity of hydrogen-induced softening in the material. The hydrogen influenced, crack front fields serve as input to an exponential-based characterization of void growth rates which provides qualitative estimates for the impact of hydrogen on tearing resistance curves. The analyses suggest significantly higher void growth rates exist in a hydrogen-charged material than in a hydrogen free material, with a corresponding reduction in tearing resistance in the presence of hydrogen regardless of the level of imposed constraint. [Copyright &y& Elsevier]

Abstract: This paper deals with a finite element algorithm for the creep crack growth process in a viscoelastic medium. The main developments focus on the coupling between the M-integral and an incremental formulation for the viscoelastic behavior. In this context, mixed mode configurations are simulated for orthotropic symmetries. An algorithm uncoupling viscoelastic incremental formulation and the fracture procedure is resolved with finite element software. The global approach is validated in terms of the evolution of energy release rate versus time and the advance of cracks. Numerical simulations are based on a Constant Tension Shear model. The insensitivity of the M-integral to the integration domain is shown from creep crack growth simulations for mixed mode configurations. [Copyright &y& Elsevier]

Abstract: The determination of relevant constitutive crack propagation laws under dynamic loading is a rather challenging exercise. In dynamic impact cases, the variations of propagation parameters and the extractions of crack positions are difficult tasks. This paper focuses on a methodology for assessing dynamic crack propagation laws under impact loading for transparent materials. Dynamic brittle fracture experiments are performed on polymethyl methacrylate (PMMA) in which several crack arrest phases occur. Then, these experiments are numerically reproduced by using the eXtended Finite Element Method (X-FEM) in order to validate the algorithms and the criteria assumed. [Copyright &y& Elsevier]

Abstract: In the framework of numerical analysis of joined bodies, the present paper is devoted to the constitutive modeling, via an interface kinematic formulation, of mechanical behaviour of internal adhesive layers. The proposed interface constitutive model couples a cohesive behaviour, based on the damage mechanics theory, with a frictional one, defined in a non-associative plasticity framework. Namely, the interface formulation follows the transition of the adhesive material from the sound elastic condition to the fully cracked one. This formulation is able to model, by means of a specific interpretation of the damage variable and in a relevant mathematical setting, the interface intermediate mechanical properties, during the microcracks spreading process up to the discontinuity surface formation (macrocrack). The constitutive modeling is performed in fully compliance with the thermodynamic principles, in order to ensure the thermodynamic consistency requirement. In the present work, various monotonic and cyclic loading conditions are examined in order to show the main features of the constitutive formulation as well as several significant differences with respect to other existing models. Computational efficiency of the interface constitutive model is tested in a numerical application by FEM resolution strategy approach. [Copyright &y& Elsevier]

Tracking the crack propagation in concrete at the mesoscopic level is of great importance for revealing the crack pattern and failure mechanism, due to the huge threat of cracking to structure safety. This paper develops a phase field modeling scheme with mesostructure of concrete composite to investigate its crack propagation behavior. With the classical phase field model and the staggered algorithm implementation by three-dimensional (3D) finite element method (FEM), crack propagation within concrete's mesostructure composed of coarse aggregate, mortar matrix, interfacial transition zone (ITZ) and initial defects including micropores and microcracks is modeled. The proposed modeling scheme is tested on single-aggregate samples and complex mesostructured concrete samples subjected to uniaxial loading, showing reasonable accordance with the experimental observation and common failure modes of concrete material. The results indicate that mesostructural configurations are important factors affecting the crack pattern of concrete. The presence of coarse aggregates is prone to initiate and induce interfacial cracking in the ITZ effect, but also exerts the blocking effect on the crack growth. And the initial defects (micropores and microcracks) are also the important influential factor on crack initiation, propagation and the formation of the major crack. It is found that the higher the volume fractions of aggregates and initial defects, the cracking of concrete initiates earlier, propagates faster and penetrates more easily when subjected to the same loading condition. [ABSTRACT FROM AUTHOR]

Abstract: This paper focuses on modeling of the interface between a rigid substrate and a thin elastic adherend subjected to mixed-mode loading in the peel test configuration. The context in which the investigation is situated is the study of bond between fiber-reinforced polymer (FRP) sheets and quasi-brittle substrates, where FRP sheets are used as a strengthening system for existing structures. The problem is approached both analytically and numerically. The analytical model is based on the linear-elastic fracture mechanics energy approach. In the numerical model, the interface is discretized with zero-thickness contact elements which account for both debonding and contact within a unified framework, using the node-to-segment contact strategy. Uncoupled cohesive interface constitutive laws are adopted in the normal and tangential directions. The formulation is implemented and tested using the finite element code FEAP. The models are able to predict the response of the bonded joint as a function of the main parameters, which are identified through dimensional analysis. The main objective is to compute the debonding load and the effective bond length of the adherend, i.e., the value of bond length beyond which a further increase has no effect on the debonding load, as functions of the peel angle. The detailed distributions of interfacial shear and normal stresses are also found. Numerical results and analytical predictions are shown to be in excellent agreement. [Copyright &y& Elsevier]

Abstract: The fractal-like finite element method has been proved to be very efficient and accurate in two-dimensional static and dynamic crack problems. In this paper, we extend our previous study to include the thermal effect for two-dimensional isotropic thermal crack problems. Both the temperature intensity factor and thermal stress intensity factor can be calculated directly. The temperature distribution is first found, which is imposed thereafter as a thermal load in the elastic problem. The transformation function used in the study has been found analytically. The effects of different thermal loading on the thermal stress intensity factor are presented. The numerical examples are compared with the results from other methods and find to be in good agreement. [Copyright &y& Elsevier]