The “Calcaires du Barrois” Formation is a succession of dominantly micritic limestone of Kimmeridgian to Tithonian age, outcropping in the eastern part of the Paris Basin. This is an active karstic aquifer of main interest for the Andra (French National Agency for Radioactive Waste Management) who study the feasibility of a deep geological repository of radioactive waste in an Underground Research Laboratory (URL) located approximately 450m below the surface. Surface installations of the CIGEO (Industrial Centre for Geological Disposal) project are planned to be located in the upstream recharge zone of the aquifer. It is of primary interest to characterise the “Calcaires du Barrois” Formation to provide guidelines for the planning and the sizing of these facilities, with the objective of minimising the impact on the aquifer system. An integrated study was designed for this purpose linking petrography (thin section, and SEM, Scanning Electron Microscope), C & O stable isotope geochemistry, XRD (X-Ray Diffraction), petrophysics and geomechanics, and based on the analysis of three key cored wells penetrating the formation at different relative depths. The “Calcaires du Barrois” underwent several stages of diagenesis that defined the current properties. Unconformities associated with the Jurassic-Cretaceous transition led to prolonged early subaerial exposures during which freshwater flowed efficiently through the upper half of the formation. Through mineralogical stabilisation, among other processes, microporosity was preserved in micrites in this interval consisting of clean limestone with thin marl layers. The lower half of the formation, more argillaceous, was not or only slightly affected by this early meteoric diagenesis and recrystallization and cementation of micrites occurred during burial diagenesis, involving chemical compaction. Later, during the return to the surface associated to the Cenozoic orogens, another phase of meteoric diagenesis affected the uppermost few metres below the outcropping portions of the formation, but without modifying significantly the previously acquired petrophysical properties. Consequently, an intra-formational boundary was progressively developed at around 75m (from the top reference). This boundary separates (1) a lower half of the “Calcaires du Barrois” with dense and tight micrites, showing high Young's Modulus values, and a moderate intensity of fractures, from (2) a upper half with microporous micrites showing low Young's Modulus values, and almost devoid of fractures. A transitional zone of about 30m-thick, with intermediate properties, sitting above this boundary and below the only thin metre-scale macroporous grainstone level of the formation, accommodated most of the deformation linked to the Cenozoic west-European orogens and is intensively fractured. The current hydrogeological model considers a purely sedimentological boundary to delimit two sub-aquifers within the “Calcaires du Barrois” Formation, but will have to be reappraised since it is here demonstrated that the real boundary is located significantly higher in the formation and is inherited from a multi-stage diagenetic history. These findings will complement and influence planning for engineering of the CIGEO project.

Size-effect in concrete and other quasi-brittle materials defines the relation between the nominal strength and structural size when material fractures. The main cause of size-effect is the so-called energetic size-effect which results from the release of the stored energy in the structure into the fracture front. In quasi-brittle materials and in contrast to brittle materials, the size of the fracture process zone is non-negligible compared to the structural size. As a consequence, the resulting size-effect law is non-linear and deviates from the response predicted by linear elastic fracture mechanics. In order to simulate the size-effect, one needs to rely on numerical modeling to describe the formation, development and propagation of the fracture process zone. Although a number of models have been proposed over the years, it transpires that a correct description of the fracture and size-effect which accounts for boundary effects and varying structural geometry remains challenging. In this study, the Lattice Discrete Particle Model (LDPM) is proposed to investigate the effects of structural dimension and geometry on the nominal strength and fracturing process in concrete. LDPM simulates concrete at the aggregate level and has shown superior capabilities in simulating complex cracking mechanisms thanks to the inherent discrete nature of the model. In order to evaluate concrete size-effect and provide a solid validation of LDPM, one of the most complete experimental data set available in the literature was considered and includes three-point bending tests on notched and unnotched beams. The model parameters were first calibrated on a single size notched beam under three-point bending and on the mechanical response under unconfined compression. LDPM was then used to perform blind predictions on the load-crack mouth opening displacement curves of different beam sizes and notch lengths. Splitting test results on cylinders were also predicted. The results show a very good agreement with the experimental data. The quality of the predictions was quantitatively assessed. In addition, a discussion on the fracturing process and dissipated energy is provided. Last but not least, the Universal Size-Effect Law proposed by Bažant and coworkers was used to estimate concrete fracture parameters based on experimental and numerical data.

This paper addresses the calculation of the relative permeability of concrete and rocks with a model that is aimed at being implemented in large scale computations for evaluating the tightness of vessels. To this end, it is necessary to rely on some fast procedure and a random hierarchical capillary approach is used. It is based on the extension of an existing model proposed initially to describe the evolution of the intrinsic permeability of mortar undergoing micro-cracking. First, the efficiency of this existing model is tested on several types of concretes and rocks, with permeability spanning over 6 orders of magnitude. Then, the model is adapted to obtain the relative permeability to gas and liquid as a function of the saturation of the porous solid with respect to the liquid phase. The extended model is shown to provide reasonably accurate predictions for several concretes and rocks tested in the literature.

A hydro-mechanical coupled lattice-based model for the simulation of crack propagation induced by fluid injection in porous saturated rocks containing cohesive joints is presented. Rock follows an isotropic damage model for tensile fracture and cohesive joints follow a coupled plasticity- damage model. The discretisation uses a dual lattice approach: a Delaunay triangulation for the solid and the boundaries of the associated Voronoï tesselation for the hydraulic part. A classical poromechanical framework for a materials saturated with a single fluid is implemented. First, predictions of crack propagation are compared with analytical models. Then, the interaction between a propagating crack and an existing joint is analysed. Two configurations are con- sidered: the case of a joint that is orthogonal to the crack path and the case of a joint that is inclined by 45° with respect to the crack path. For the vertical joint, the crack is first arrested because the cohesive joint is weaker than the rock mass. The crack reinitiates at both crack tips and subsequently propagates in one of them. For the inclined joint, the crack follows the joint and therefore its path is deviated. Damage in the rock develops in the back of the crack tip, thereby enhancing the increase of permeability due to damage in the rock mass.

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Measuring the permeability of tight rocks remains a challenging task. In addition to the traditional sources of errors that affect more permeable formations (e.g. sample selection, non-representative specimens, disturbance introduced during sample acquisition and preparation), tight rocks can be particularly prone to solid–fluid interactions and thus more sensitive to the methods, procedures and techniques used to measure permeability. To address this problem, it is desirable to collect, for a single material, measurements obtained by different methods and pore-fluids. For that purpose a collaborative benchmarking exercise involving 24 laboratories was organized for measuring the permeability of a single low permeability material, the Grimsel granodiorite, at a common effective confining pressure (5 MPa). The objectives of the benchmark were: (i) to compare the results for a given method, (ii) to compare the results between different methods, (iii) to analyze the accuracy of each method, (iv) to study the influence of experimental conditions (especially the nature of pore fluid), (v) to discuss the relevance of indirect methods and models and finally (vi) to suggest good practice for low permeability measurements. In total 39 measurements were collected that allowed us to discuss the influence of (i) pore-fluid, (ii) measurement method, (iii) sample size and (iv) pressure sensitivity. Discarding some outliers from the bulk data set (4 out of 39) an average permeability of 1.11 × 10−18 m² with a standard deviation of 0.57 × 10−18 m² was obtained. The most striking result was the large difference in permeability for gas measurements compared to liquid measurements. Regardless of the method used, gas permeability was higher than liquid permeability by a factor approximately 2 (kgas = 1.28 × 10−18 m² compared to kliquid = 0.65 × 10−18 m²). Possible explanations are that (i) liquid permeability was underestimated due to fluid-rock interactions (ii) gas permeability was overestimated due to insufficient correction for gas slippage and/or (iii) gases and liquids do not probe exactly the same porous networks. The analysis of Knudsen numbers shows that the gas permeability measurements were performed in conditions for which the Klinkenberg correction is sufficient. Smaller samples had a larger scatter of permeability values, suggesting that their volume were below the Representative Elementary Volume. The pressure dependence of permeability was studied by some of the participating teams in the range 1–30 MPa and could be fitted to an exponential law k = ko.exp(–γPeff) with γ = 0.093 MPa−1. Good practice rules for measuring permeability in tight materials are also provided.

Measuring and modelling the permeability of tight rocks remains a challenging task. In addition to the traditional sources of errors that affect more permeable formations (e.g. sample selection, non-representative specimens, disturbance introduced during sample acquisition and preparation), tight rocks can be particularly prone to solid–fluid interactions and thus more sensitive to the methods, procedures and techniques used to measure permeability. To address this problem, it is desirable to collect, for a single material, measurements obtained by different methods and pore fluids. For that purpose, a benchmarking exercise involving 24 laboratories was organized for measuring and modelling the permeability of a single low-permeability material, the Grimsel granodiorite. The objectives of the benchmark were: (i) to compare the results for a given method, (ii) to compare the results between different methods, (iii) to analyse the accuracy of each method, (iv) to study the influence of experimental conditions (especially the nature of pore fluid), (v) to discuss the relevance of indirect methods and models and finally (vi) to suggest good practice for low-permeability measurements. To complement the data set of permeability measurements presented in a companion paper, we focus here on (i) quantitative analysis of microstructures and pore size distribution, (ii) permeability modelling and (iii) complementary measurements of permeability anisotropy and poroelastic parameters. Broad ion beam—scanning electron microscopy, micro-computerized tomography, mercury injection capillary pressure (MICP) and nuclear magnetic resonance (NMR) methods were used to characterize the microstructures and provided the input parameters for permeability modelling. Several models were used: (i) basic statistical models, (ii) 3-D pore network and effective medium models, (iii) percolation model using MICP data and (iv) free-fluid model using NMR data. The models were generally successful in predicting the actual range of measured permeability. Statistical models overestimate the permeability because they do not adequately account for the heterogeneity of the crack network. Pore network and effective medium models provide additional constraints on crack parameters such as aspect ratio, aperture, density and connectivity. MICP and advanced microscopy techniques are very useful tools providing important input data for permeability estimation. Permeability measured—orthogonal to foliation is lower that—parallel to foliation. Combining the experimental and modelling results provide a unique and rich data set.

Size and shape effects are important issues in predicting the global response of concrete structures. Small-scale tests performed in laboratory to determine the material properties are not enough to simulate large-scale structures. Many models are used to extrapolatesmall scale results to large scale simulations, but only few are able to recover size and shape effects. Recently a model of graded damage (TLS) has been proposed and comparison with cohesive zone models shows that this new model contains a new degree of freedom,the length of transition between totally damaged material and undamaged zone (ie the process zone size). In this paper, the capability of the model (TLS) to represent size and shape effects for two recently published experimental campaigns is studied.

In this paper, the fracture process zone (FPZ) is investigated on unnotched and notched beams with different notch depths. Three-point bending tests have been realized on plain concrete under crack mouth opening displacement (CMOD) control. Crack growth is monitored by applying the acoustic emission (AE) technique. The comparison with a numerical model is also realized by using a mesoscopic approach. Such an approach is of particular interest in the analysis of interactions between the cementitious matrix and aggregates. Several AE parameters are examined during the entire loading process, and show that the relative notch depth influences the AE characteristics, the process of crack propagation, and the brittleness of concrete. The numerical load-CMOD curves show that the mesoscopic modelling reproduces well the notch effect and concrete failure. In order to improve our understanding of the FPZ, the width and length of the FPZ are followed based on the AE source locations maps in parallel with the numerical damage fields. An important energy dissipation is observed at the crack initiation in unnotched beams.

Characterizing the path of a hydraulic fracture in a heterogeneous medium is one of the challenges of current research on hydraulic fracturing. We present here a 2D lattice hydro-mechanical model for this purpose. Natural joints are represented introducing elements with a plastic-damage behaviour. The action of fluid pressure on skeleton is represented using Biot’s theory. The interactions of cracks on fluid flow are represented considering a Poisueille’s flow between two parallel plates. The model is simplified by neglecting the effect of deformation in the equation governing fluid flow. Numerical coupling is achieved with a staggered coupling scheme. We consider first the propagation of fracture restricted to the homogeneous case. The numerical model is compared to analytical solutions. It is found that the model is consistent with LEFM in the pure mechanical case, and with analytical solutions from the literature in the case where the leak off is dominant. In very tight formations, deviations are observed, as expected, because of the assumption in the flow model. Finally, the influence of a natural joint of finite length crossed by the fracture is shown. Two cases are considered, the case of a joint perpendicular to the crack and the case of an inclined joint. In the first case, the crack passes through the joint, which is damaged due to the intrusion of the fluid. In the second case, the crack follows the joint and propagation starts again from the tip.

The degradation of quasi-brittle materials encompasses micro-cracks propagation, interaction and coalescence in order to form a macro-crack. These phenomena are located within the Fracture Process Zone (FPZ). This paper aims at providing a further insight in the description of the FPZ evolution with the help of statistical analysis of damage. The statistical analysis relies on the implementation of Ripley’s functions, which have been developed in order to exhibit patterns in image analyses. It is shown how a correlation length may be extracted from the Ripley’s function analysis. Comparisons between experimental and numerical evolutions of extracted correlation lengths are performed.

A new calibration strategy for integral-type nonlocal damage models for quasi-brittle materials is proposed. It is based on the assumption that in the fracture process zone in quasi-brittle materials the large majority of energy is dissipated in a localised rough crack. Measuring the roughness of the fracture surface allows for calibrating the interaction radius of nonlocal models by matching experimental and numerical standard deviations of spatial distributions of dissipated energy densities. Firstly, fracture analyses with a lattice model with random fields for strength and fracture energy are used to support the assumptions of the calibration process. Then, the calibration strategy is applied to an integral-type nonlocal damage model for the case of a fracture surface of a three-point bending test.

A simplified model based on capillary bundle aimed at computing the intrinsic and the apparent permeabilities of mortar to gas is presented. At the micro-level of capillaries, fluid flow follows the classical Poiseuille’s law combined with Knudsen’s flow. At the macro-level, the equation governing fluid flow is very similar to Klinkenberg’s model, and exhibits a dependence of the apparent permeability to the mean pressure. The input data entering in the analytical model are the pore size distributions directly measured from mercury intrusion porosimetry cut above a threshold diameter in order to avoid the overestimation of the permeability inherent to the bundle model. The model is fitted on experimental data on mortar specimens subjected to damage due to electrical fracturing and a tortuosity factor is identified. Fits on the same material with different states of damage show that the tortuosity decreases as damage progresses.

The fracture process zone (FPZ) was investigated on unnotched and notched beams with different notch depths. Three point bending tests were realized on plain concrete under crack mouth opening displacement (CMOD) control. Crack growth was monitored by applying the acoustic emission (AE) technique. In order to improve our understanding of the FPZ, the width and length of the FPZ were followed based on the AE source locations maps and several AE parameters were studied during the entire loading process. The bvalue analysis, defined as the log-linear slope of the frequency-magnitude distribution of acoustic emissions, was also carried out to describe quantitatively the influence of the relative notch depth on the fracture process. Theresults show that the number of AE hits increased with the decrease of the relative notch depth and an important AE energy dissipation was observed at the crack initiation in unnotched beams. In addition, the relative notch depth influenced the AE characteristics, the process of crack propagation, and the brittleness of concrete.

The purpose of this paper is to analyse the development and the evolution of the fracture process zone during fracture and damage in quasi-brittle materials. A model taking into account the material details at the mesoscale is used to describe the failure process at the scale of the heterogeneities. This model is used to compute histograms of the relative distances between damaged points. These numerical results are compared with experimental data, where the damage evolution is monitored using acoustic emissions. Histograms of the relative distances between damage events in the numerical calculations and acoustic events in the experiments exhibit good agreement. It is shown that the mesoscale model provides relevant information from the point of view of both global responses and the local failure process.

The degradation of quasi-brittle materials encompasses micro-crack propagation, interaction and coalescence in order to form a macro-crack. These phenomena are located progressively within the so-called Fracture Process Zone (FPZ). The shape and growth of the FPZ, and its interaction with boundaries lead to typical phenomena such as size effects, boundary effects and shielding effects. Classical failure constitutive models involve strain softening due to progressive cracking and a regularization technique for avoiding spurious strain and damage localization. Different approaches have been promoted in the literature such as integral-type non-local models, gradient damage formulations, cohesive cracks models or strong discontinuity approaches. Such macroscale failure models have been applied on a wide range of problems, including the description of damage and failure in strain softening quasi-brittle materials, softening plasticity, creep or composite degradation. An important element of validation of failure models is that they should be able to capture size and boundary effects for various geometries. However, numerical predictions of size effect on different geometries or the description of boundary effects are quite rare in the literature because experimental data on different specimen geometries and on the same material are not available for comparison. If experiments involving size effect are numerous in the literature, they are restricted to a specific geometry and barely consider structures made of the same material, with different geometries. Most of the time, the notch-to-depth ratio tends to zero without reaching zero and unnotched specimens are studied separately, with different materials compared with size effect tests on notched specimens. This paper aims at presenting new experimental and numerical investigations of failure for geometrically similar notched and unnotched concrete specimens made of the same mix. Different geometries (four depth and three notch sizes) have been considered to obtain results involving size and boundary effects at the same time. A mesomodel is used to study the FPZ evolution upon damage depending on the geometry and boundary conditions. A very good agreement with the experimental results is obtained. An analysis of the correlations involved during the fracture process at the mesoscale is performed and a good agreement with acoustic emissions data is revealed.

Failure of quasi-brittle materials such as concrete needs a proper description of strain softening due to progressive micro-cracking and the introduction of an internal length in the constitutive model in order to achieve non zero energy dissipation. This paper reviews the main results obtained with the non local damage model, which has been among the precursors of such models. In most cases up to now, the internal length has been considered as a constant. There is today a consensus that it should not be the case as models possess severe shortcomings such as incorrect averaging near the boundaries of the solid considered and non local transmission across non convex boundaries. An interaction-based model in which the weight function is constructed from the analysis of interaction has been proposed. It avoids empirical descriptions of the evolution of the internal length. This model is also recalled and further documented. Additional results dealing with spalling failure are discussed. Finally, it is pointed out that this model provides an asymptotic description of complete failure, which is consistent with fracture mechanics.

Modelling failure in geomaterials, concrete or other quasi-brittle materials and proper accounting for size effect, geometry and boundary effects are still pending issues. Regularised failure models are capable of describing size effect on specimens with a specific geometry, but extrapolations to other geometries are rare, mostly because experimental data presenting size effect for different geometries and for the same material are lacking. Three-point bending fracture tests of geometrically similar notched and unnotched specimens are presented. The experimental results are compared with numerical simulations performed with an integral-type non-local model. Comparisons illustrate the shortcomings of this classical formulation, which fails to describe size effect over the investigated range of geometries and sizes. Finally, experimental results are also compared with the universal size effect law.

CO2 capture and geological storage is seen as the most effective technology to rapidly reduce the emission of greenhouse gases into the atmosphere. Up until now and before proceeding to an industrial development of this technology, laboratory research has been conducted for several years and pilot projects have been launched. So far, these studies have mainly focused on transport and geochemical issues and few studies have been dedicated to the geomechanical issues in CO2 storage facilities. The purpose of this book is to give an overview of the multiphysics processes occurring in CO2 storage facilities, with particular attention given to coupled geomechanical problems. The book is divided into three parts. The first part is dedicated to transport processes and focuses on the efficiency of the storage complex and the evaluation of possible leakage paths. The second part deals with issues related to reservoir injectivity and the presence of fractures and occurrence of damage. The final part of the book concerns the serviceability and ageing of the geomaterials whose poromechanical properties may be altered by contact with the injected reactive fluid.

The purpose of this paper is to present a new macroscopic approach to describe the evolving non-local interactions which are produced at the mesoscale dur- ing damage and failure in quasi-brittle materials. A new-integral type non-local model is provided where the weight function is directly built from these interac- tions, and therefore takes into account their evolution during the material failure intrinsically.

The size effect on the fracture process zone in notched and unnotched three point bending tests of concrete beams is analysed by a meso-scale approach. Concrete is modelled at the meso-scale as stiff aggregates embedded in a soft matrix separated by weak interfaces. The mechanical response of the three phases is modelled by a discrete lattice approach. The model parameters were chosen so that the global model response in the form of load-crack mouth opening displacement curves were in agreement with experimental results reported in the literature. The fracture process zone of concrete is determined numerically by evaluating the average of spatial distribution of dissipated energy densities of random meso-scale analyses. The influence of size and boundary conditions on the fracture process zone in concrete is investigated by comparing the results for beams of different sizes and boundary conditions.

The purpose of this paper is to discuss how boundary and emerging boundary effects can be folded into a new non-local damage formulation based on integral models that provides a consistent transition towards discrete cracking. Several enhancements of the original non-local damage model inspired from micromechanics of interacting defects are considered. The goals of the modified non-local formulation are threefold: (1) the distribution of damage at failure should be mesh independent; (2) the model should be able to capture the continuous/discontinuous transition involved in the process of failure due to increasing stresses; (3) the discontinuous displacements fields resulting from complete failure should be approached as closely as possible. A one dimensional example illustrates the capabilities of the original and enhanced models. It is found that a combination of increasing/decreasing interactions and non-local effects during failure provides the most suitable results.

The book, prepared in honor of the retirement of Professor J. Mazars, provides a wide overview of continuum damage modeling applied to cementitious materials. It starts from micro-nanoscale analyses, then follows on to continuum approaches and computational issues. The final part of the book presents industry-based case studies. The contents emphasize multiscale and coupled approaches toward the serviceability and the safety of concrete structures.

This paper is devoted to the numerical simulation of dynamic crack propagation using X-FEM and level set techniques. The paper proposes an explanation of three experiments. The first experiment shows the dynamic propagation of a crack that avoids a hole placed on its trajectory. The second presents the interpretation of experiments of two crack tips which run in the same direction, and the third studies the interaction between two cracks which move toward each other. It is shown in all the cases that the crack tip avoids the other discontinuity (hole or other crack tip). An explanation is proposed through the observation of transient stress fields.

This work examines the performance of composite panels when subjected to underwater impulsive loads. The scaled fluid-structure experimental methodology developed by Espinosa and co-workers was employed. Failure modes, damage mechanisms and their distributions were identified and quantified for composite monolithic and sandwich panels subjected to typical blast loadings. The temporal evolutions of panel deflection and center deflection histories were obtained from shadow Moiré fringes acquired in real time by means of high speed photography. A linear relationship of zero intercept between peak center deflections versus applied impulse per areal mass was obtained for composite monolithic panels. For composite sandwich panels, the relationship between maximum center deflection versus applied impulse per areal mass was found to be approximately bilinear but with a higher slope. Performance improvement of sandwich versus monolithic composite panels was, therefore, established specially at sufficiently high impulses per areal mass (I0/M¯>170 m s−1). Severe failure was observed in solid panels subjected to impulses per areal mass larger than 300 m s−1. Extensive fiber fracture occurred in the center of the panels, where cracks formed a cross pattern through the plate thickness and delamination was very extensive on the sample edges due to bending effects. Similar levels of damage were observed in sandwich panels but at much higher impulses per areal mass. The experimental work reported in this paper encompasses not only characterization of the dynamic performance of monolithic and sandwich panels but also post-mortem characterization by means of both non-destructive and microscopy techniques. The spatial distribution of delamination and matrix cracking were quantified, as a function of applied impulse, in both monolithic and sandwich panels. The extent of core crushing was also quantified in the case of sandwich panels. The quantified variables represent ideal metrics against which model predictive capabilities can be assessed.

The determination of relevant constitutive crack propagation laws under dynamic loading is a rather challenging operation. In dynamic impact cases, the variations of propagation parameters and exact crack positions are difficult to control. This paper focuses on different techniques for measuring accurate crack tip position histories in dynamic crack propagation experiments. Two different methods are considered: very accurate crack tip localization by optical displacement sensors is first described for transparent materials; then, an automatic method based on digital image correlation is presented for crack localization in all brittle materials whatever their opacity.

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.

Our purpose is to propose a methodology for assessing dynamic crack propagation laws under mixed-mode loading. Dynamic brittle fracture experiments are performed on polymethylmethacrylate (PMMA) in which mode combination changes and 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.

This paper is devoted to the simulation of dynamic brittle crack propagation in an isotropic medium. It focuses on cases where the crack deviates from a straight-line trajectory and goes through stop-and-restart stages. Our argument is that standard methods such as element deletion or remeshing, although easy to use and implement, are not robust tools for this type of simulation essentially because they do not enable one to assess local energy conservation. Standard cohesive zone models behave much better when the crack’s path is known in advance, but are difficult to use when the crack’s path is unknown. The simplest method which consists in placing the cohesive segments along the sides of the finite elements leads to crack trajectories which are mesh-sensitive. The adaptive cohesive element formulation, which adds new cohesive elements when the crack propagates, is shown to have the proper energy conservation properties during remeshing. We show that the X-FEM is a good candidate for the simulation of complex dynamic crack propagation. A two-dimensional version of the proposed X-FEM approach is validated against dynamic experiments on a brittle isotropic plate.

The objective of this paper is to describe a simple dynamic crack propagation experiment which reproduces two phenomena: mixed-mode propagation and crack stop and restart. This experiment is explained and interpreted using X-FEM simulations. We show that a simple fracture theory which consists in using a dynamic crack initiation toughness, a crack orientation along the maximum principal stress and a simple equation for the calculation of the crack speed is sufficient to explain what is observed experimentally.