Discrete Crack Research Articles

An efficient moving-mesh strategy for predicting crack propagation in unidirectional composites: Application to materials reinforced with aligned CNTs

This paper presents an efficient numerical approach for reproducing the process of crack propagation inside unidirectional composites subjected to general loading conditions, with special reference to epoxy materials enhanced with embedded aligned CNTs. This approach involves a traditional FE framework improved by the Moving Mesh (MM) technique based on the Arbitrary Lagrangian-Eulerian (ALE) formulation and the Interaction Integral Method (M−integral). The MM serves as a powerful numerical tool to simulate the discrete crack advance with minimal remeshing, thus reducing the computational complexities. Instead, the M−Integral method, formulated for generally anisotropic materials, has been employed to extract the mixed-mode Stress Intensity Factors (SIFs), which are necessary to define the crack onset condition and propagation direction on the basis of the modified Maximum Hoop Stress Criterion. The proposed strategy includes the extended rule of mixtures to evaluate the homogenized elastic properties of nano-reinforced composites. The validity of the proposed methodology has been assessed through comparisons with experimental data and numerical results available in the literature.

A coupled phase-field model for sulfate-induced concrete cracking

The performance of concrete will decrease when subjected to external sulfate corrosion, and numerical models are effective means to analyze the mechanism. Most models cannot efficiently consider the effect between cracks and ionic transport because crack initiation and propagation are ignored. In this paper, a coupled chemical-transport-mechanical phase-field model is developed, in which the phase-field model is applied for the first time to predicate the cracking of sulfate-eroded concrete. The chemical-transport model is established based on the law of conservation of mass and chemical kinetics. The phase-field model equivalents the discrete sharp crack surface into a regularized crack, making it convenient to couple with the chemical-transport model. The crack driving energy in the phase-field model is computed by the expansion strain, which can be obtained from the chemical-transport model. The coupling of crack propagation and ionic transport is achieved by a theoretical equation, which considers both the effects of cracking and porosity. Complex erosion cracks can be automatically tracked by solving the phase-field model. The simulation results of the multi-field coupling model proposed in this paper are in good agreement with the experimental data. More importantly, the spalling phenomenon observed in physical experiments is reproduced, which has not been reported by any other numerical models yet, and new insight into the spalling mechanism is provided.

Three dimensional simulations of FRC beams and panels with explicit definition of fibres-concrete interaction

High performance concrete (HPC) is a quite novel material which has been rapidly developed in the last few decades. It exhibits superior mechanical properties and durability comparing to normal concrete. HPC can achieve also superior tensile performance if strong fibres (steel or carbon) are implemented in the matrix. Thus, there exist the unabated interest in studying how the addition of different types of fibres modifies the behaviour of HPC. Nowadays, a standard numerical approaches to model the behaviour of fibre reinforced concrete (FRC) are carried out by means of the smeared or discrete crack modelling of homogenous media with appropriately changed stress-strain relationships. The objective of this paper is to develop a new and efficient mesoscale modelling approach for steel fibre reinforced high-performance concrete. The main idea of presented approach is to assume the fully 3D modelling with taking into account explicitly the distribution and orientation of the steel fibres. As a benchmark, results obtained from experimental campaign on beams and panels made from high-performance concrete with steel fibres of different sizes and dosages were taken. Results of numerical simulations were directly compared with experimental outcomes in order to validate and calibrate FE-model and to introduce the efficient numerical modelling tool.

A fibre direction informed continuum damage model with enriched kinematics for modelling matrix cracking in composites

Continuum Damage Mechanics models are widely used for simulation of ply-level damage such as matrix cracking in composites. Although their ease of implementation within the finite element framework is appealing, several limitations exist such as a smeared representation of sharp cracks, mesh orientation bias of crack growth, inaccurate energy dissipation due to approximate definition of characteristic length etc. In this work, a new ‘semi-discrete’ continuum damage model is proposed for matrix cracking, that includes sharp crack kinematics. The mesh orientation bias is eliminated by a fibre-directed growth driving criterion. The crack characteristic length is exactly computed due to an accurate geometric representation of the crack surface. The model also addresses a well-known problem of spurious stress transfer across crack faces when deformation becomes large. Through several challenging benchmark problems, the model is shown to perform nearly as good as discrete crack models while being simpler and more robust.

Post-earthquake fire performance of partially encased composite steel and concrete columns

Considering the potential severity of losses caused by post-earthquake fires compared to earthquakes alone, this study employed a three-dimensional Finite Element (FE) model established in ABAQUS to investigate the response of partially encased composite (PEC) steel and concrete columns under post-earthquake fire, serving as preliminary analysis for subsequent experimental studies. The validity of the FE model was verified using results from existing seismic and fire loading tests. In simulating the hysteresis behavior of PEC columns, this study evaluated the impacts of concrete discrete cracking and mechanical models on the simulation outcomes, thereby refining the modeling technique. A typical PEC column was selected as the focus of this investigation. Sequential earthquake-fire simulations were conducted using a data transfer technique to assess the fire resistance performance of different seismic damaged columns with different axial compression load ratios. The results indicate that the behavior of damaged PEC columns evolves based on initial damage, and the failure exhibits overall bending accompanied by local buckling of the steel flange. As the axial load ratio increases, the fire resistance time of seismic-damaged PEC columns significantly decreases. When the axial compression ratio is increased from 0.2 to 0.5, the fire resistance time of columns with damage factor D within 0.6 decreases by 59.07% on average. This sensitivity to axial pressure is particularly pronounced when earthquake damage is severe. Moreover, it finds that the lateral drift ratio under seismic action should be controlled within 2% to ensure that the post-earthquake fire resistance will not be significantly reduced.

Maximum energy dissipation-based incremental approach for structural analyses involving discrete fracture propagation in quasi-brittle materials

A maximum energy dissipation-based incremental approach (MEDIA) is proposed to overcome limit points, e.g. strong snap-backs, in the fracture analysis of quasi-brittle materials. An optimisation step is applied using an expression proposed to compute the change of dissipated energy within the discretised body when moving from one state of equilibrium to another. This expression is developed at the integration point level and uses a binary pathway vector to define all the possible solutions within that step. Due to the unique way the problem is cast, a genetic algorithm is deployed to identify the solution leading to the highest energy dissipation while following applicable thermodynamic constraints. The resulting analysis is non-iterative and purely incremental. MEDIA is particularly applicable in combination with discrete crack models. In this case, meshes are relatively coarse and each crack can be individually handled to maintain the computational cost independent of the discretisation. The equations are also cast in a direct inverse method that avoids explicitly solving the inversion of the stiffness matrices for each chromosome in the genetic optimisation. Problems having multiple snap-back effects and non-proportional loading, as well as lightly and highly reinforced concrete beams, are used to assess the suitability and efficiency of the proposed method. In contrast with other available techniques, MEDIA is shown to follow the adopted constitutive models without any energy loss due to the solution-finding process while providing adequate structural responses.

Blind competition on the numerical simulation of slabs reinforced with conventional flexural reinforcement and fibers subjected to punching loading configuration

AbstractThis paper describes the 3rd Blind Simulation Competition (BSC) organized by the fib WP 2.4.1 which aims to assess the predictive performance of models based on the finite element method (FEM) for analysis and design of fiber reinforced concrete (FRC) structures submitted to loading and support conditions that promote punching failure mode. Fiber reinforcement is used in an attempt to eliminate conventional punching reinforcement and provide technical and economic advantages. The two tested real‐size prototypes represent a column‐slab interior region of an elevated steel‐fiber reinforced concrete (E‐SFRC) slab where anti‐progressive collapse reinforcement is disposed in the alignment of columns/piles. Despite a punching failure surface being formed in both experimentally tested prototypes at the rupture stage, fiber reinforcement was able to mobilize the yield capacity of the conventional flexural reinforcement, providing high deformation capacity, and ductility to the prototypes. The average post‐peak load‐carrying capacity of the tested prototypes at a deflection seven times higher than the deflection at yield initiation of the conventional reinforcement was still 90% of the average peak load. Regarding the BSC, a total of 26 proposals were received and involved 94 participants from 29 institutions and 17 countries, with 53.9% using smeared crack models (SCMs), 30.8% a concrete damage plasticity (CDP) model, 3.8% discrete crack models (DCMs) and 11.5% considered as “other models.” From these simulations it was verified, in average terms, that SCM assured the best predictive performance apart from the average strain in the SFRC and the maximum crack width which were better predicted by DCM. More accurate predictions were obtained by using in‐house software than by adopting commercial software.

An explicit finite element discrete crack analysis of open hole tension failure in composites

Developing efficient, robust methods for predicting the progressive failure of carbon fiber composites under tension is essential for optimal design, balancing weight reduction, damage tolerance, and service life. Implicit finite element (FE) methods struggle with the complex interplay of failure mechanisms, leading to a heavy reliance on costly, time-consuming experimental testing. This study introduces a novel explicit algorithm designed for laminate-level mesh models, capable of simulating cohesive cracks without predefined paths. Utilizing an explicit finite element software approach, our method effectively addresses convergence issues associated with the non-linear and unstable nature of composite failures during quasi-static loading. Contrasting with implicit FE method, this mesh-independent approach is both practical and numerically robust. The algorithm’s performance, tested on carbon-fiber reinforced composites with varying ply configurations [452/-452]s, [45n/90n/-45n/0n]s and [45/90/-45/0]ns (n=1/2/4/8), demonstrates improved simulation accuracy and efficiency over implicit FE methods, aligning well with prior experimental and simulation data. This advancement offers a promising solution for accurately simulating and understanding the complex failure behavior of these composites.

Application of single surface isotropic damage plasticity model in nonlinear dynamic analysis of the Koyna Dam

PurposeIn the present study, the application of a recent damage plasticity model is presented for nonlinear dynamic analysis of the Koyna gravity dam. This is a single surface isotropic damage plasticity concrete model, which is based on the decomposition of stresses and was proposed in a previous study. The theoretical aspects of the model are initially reviewed, and a few preliminary verification examples are illustrated. Thereafter, the HHT-α (i.e. Hilber–Hughes–Taylor) algorithm is presented for nonlinear dynamic analysis of concrete gravity dams.Design/methodology/approachBased on the prepared tools, nonlinear behavior of the Koyna Dam is studied by applying the invoked damage plasticity model. For this purpose, three cases are considered for the present study. Case A, which is based on the linear model, is mainly used for comparative purposes. The other two cases (B and C) correspond to the nonlinear (i.e. damage plasticity) model. The basic data for these two cases are similar. However, the employed damping algorithms are different and correspond to constant and variable damping algorithms, respectively. This means that the damping matrix is either kept constant or updated for all iterations of different time increments through the course of analysis.FindingsThe time histories of horizontal displacement at the dam crest were initially compared for the three cases: the linear Case A, and two nonlinear Cases B and C. It was observed that nonlinear cases’ responses begin to deviate from the corresponding linear case after the time of about 4.3 s. However, the amount of change for Case C (i.e. variable damping) was much greater than for Case B (i.e. constant damping). This was manifested initially in the peaks of response. It was also noticed that the period of response changed slightly for Case B in comparison with the linear Case A, while this change was significant for Case C. The obtained tensile and compressive damages were subsequently compared for the two nonlinear cases. For constant damping Case B, it was noticed that tensile damage occurred in the D/S face kink and on the U/S face slightly at a lower elevation. Moreover, it had a scattered nature. However, in variable damping Case C, it was noticed that tensile damage was much more localized and acted similar to a discrete crack. Of course, both cases also show tensile damages at the dam’s heel. In regard to compressive damages, it is observed that low values are occurring for both nonlinear cases as expected.Originality/valueThe application of a recent single surface isotropic damage plasticity concrete model is presented for nonlinear dynamic analysis of the Koyna gravity dam. The nonlinear response of the dam is investigated for two different damping algorithms. Moreover, the influence of variable characteristic length is also investigated in the latter part of this study.

RC FRAME RESISTANCE TO PROGRESSIVE COLLAPSE CONSIDERING CRACK OPENING EFFECTS

In this paper, an approach is developed to account for the effect of discrete cracks on the response of reinforced concrete building frames under a column failure scenario. The approach implies the introduction of traditional finite element models of discrete ties that take into account the relationship between moments and rotations, considering the specifics of the performance of materials, sections, and structures under conditions of redistribution of forces as a result of initial local failure in the structural system of a building. Validation of the proposed approach is performed on the experimental data. Also, it is compared with the modeling results of the existing approaches. The effect of discrete cracking on the deformed state of reinforced concrete building frames under the scenario of column failure is established. The discrete cracks practically did not affect the values of axial forces in the elements. However, for bending moments within the proposed method, a decrease was observed in comparison with the traditional approach. The analysis of the diagrams shows that for reinforced concrete frames with 3 and 5 stories, there is an excess of tensile axial forces in the beam over the values according to the traditional calculation method.

Hygrothermal effects on ballistic behavior of toughened CFRP laminates

High-speed impact resistance is a critical consideration in the design and assessment of composites for aerospace applications during their service life, especially in the context of hygrothermal aging. This study, combining experiment and numerical simulation, investigates hygrothermal effects on the high-speed impact performance of a toughened T700/EH301 carbon/epoxy composite material. Three distinct hygrothermal conditions, namely Unaged, Aged, and Redried, are investigated. Experimental results reveal an apparent improvement in ballistic limit after hygrothermal aging (170.2 m/s, a notable increase of 11.2%), still maintaining an excellent performance even after redrying (158.5 m/s, an increase of 3.2%). Inspired by the micrographic analysis, a high-fidelity finite element model, referred to as HFEDCM (High Fidelity Explicit Discrete Crack Model), has been developed. This model not only explains the positive effects of hygrothermal aging on high-speed impact performance but also accurately captures the macroscopic damage morphology of composite laminates. It has been quantitatively and qualitatively demonstrated that the enhancement of the fracture toughness of the “fiber bundle” plays a critical role in improving the high-speed impact resistance of composites under hygrothermal aging.

A novel family of strain-based finite elements for the analysis of the material softening of planar frames

The article presents a novel strain-based finite element family for the analysis of material softening of planar frame structures. In our case, the softening zone is described by a discrete crack, which is considered as an ‘excluded’ finite element point, i.e., the deformation quantities in the crack are considered separately from the deformation quantities of the element. They are connected to the element only through kinematic quantities, used to describe the crack opening. The criterion for crack initiation is defined as the limit axial-bending resistance of the cross-section. The advantage of the presented model is that it is not necessary to define cracks or softening zones in advance and that the solution is mesh-independent in the sense that no further densification of the mesh is needed purely on account of capturing material softening. The accuracy and efficiency of the presented finite element family is illustrated by the example of a clamped–simply supported concrete beam and a portal concrete frame. The examples demonstrate that even with a minimum number of finite elements of suitable accuracy, sufficiently accurate results are obtained for normal engineering practice.

Parameter optimization of hot dry rock heat extraction based on discrete element crack network model

Hot-dry-rock (HDR) has long been considered a potential exploitable energy source due to its high energy content, cleanliness, and abundant reserves. However, HDR typically resides in ultra-deep strata with high temperatures and pressures, which makes its extraction a highly complex thermal-hydrological-mechanical (THM) coupling. In this paper, the THM coupling relationship in the geothermal extraction is clarified. It establishes a dynamic porosity and permeability model and creates a pair-well geothermal extraction model. The investigation focuses on understanding the influence of the pressure difference between pair-wells, number of cracks, and injection temperature on the heat extraction temperature, permeability ratio, geothermal reservoir reduction rate, and heat extraction temperature. The research findings indicate the following: (1) Increasing the inter-well pressure difference from 2 to 10 MPa reduces the extraction temperature from 155 to 138 °C. However, the thermal reservoir permeability ratio increases from 1.07 to 1.35. Consequently, the extraction efficiency rises from 6.2 to 12.4 MW. (2) The number of cracks from 200 to 400 led to a decrease in extraction temperature from 160 to 115 °C. However, the thermal reservoir permeability ratio increases from 1.12 to 1.35. In the first 8 years of extraction, the thermal pumping power of 400 cracks exceeded 200 cracks, but later this trend reversed. (3) Elevating the injection temperature from 20 to 60 °C increases the extraction temperature from 142 to 158 °C while reducing the permeability ratio from 1.28 to 1.20. Consequently, the extraction power decreases from 8 to 6 MW. (4) The inter-well pressure difference has the greatest impact on the decrease in extraction temperature, whereas the number of cracks has the greatest impact on the increase in permeability ratio. Injection temperature has the most significant impact on extraction power. This study reveals that increasing the pressure difference between wells, increasing the number of cracks, and lowering the injection fluid temperature will enhance geothermal extraction power. These findings provide valuable insights for geothermal development.

Calculation of Reinforced Concrete Frames for a Special Design Situation with Discrete Crack Modeling

Calculation of Reinforced Concrete Frames for a Special Design Situation with Discrete Crack Modeling

A diffusive‐discrete crack transition scheme for ductile fracture at finite strain

SummaryThis study presents a diffusive‐discrete crack transition scheme for stably conducting ductile fracture simulations within a finite strain framework. In the developed scheme, the crack initiation and propagation processes are determined according to an energy minimization problem based on crack phase‐field theory, and the predicted diffusive path is transformed to a discrete representation using the finite cover method during the staggered iterative scheme. In particular, for stably conducting ductile fracture simulations, three computational techniques, the staggered iterative configuration update technique, the subincremental damage update technique, and the crack opening stabilization technique, are introduced. The first and second techniques can be used regardless of whether discrete cracks are considered, and the third technique is specialized for diffusive‐discrete crack transition schemes. Accordingly, ductile fracture simulations with the developed scheme rarely encounter troublesome problems such as oscillations in the displacement field and severe distortion of finite elements that can lead to divergence of calculations. After the crack phase‐field model for ductile fractures is formulated and discretized, the numerical algorithms for realizing the diffusive‐discrete crack transition while maintaining computational stability are explained. Several representative numerical examples are presented to demonstrate the performance and capabilities of the developed approach.

A 3D multi-phase-field model for orientation-dependent complex crack interaction in fiber-reinforced composite laminates

We formulate a 3D multi-phase field model to simulate bulk and interfacial fracture in fiber-reinforced composites. The purpose of this study is to predict the complex crack interaction between the interlaminar and intralaminar fracture in FRPCs. For that, the discrete crack and the sharp interface are both smeared using the phase-field approach. A second-order anisotropic tensor is incorporated in the elastic as well as the fracture surface energy to promote direction-dependent crack growth. The interface constitutive behavior is represented by the uncoupled 3D traction–separation laws—in exponential and bi-linear form. The proposed model captures the complicated failure phenomena in FRPCs such as matrix damage, interfacial delamination, and their interactions for different configurations of lamina with different fiber orientations and fracture energies. This model’s capability is further illustrated to study the three common modes of fracture i.e. modes I, II, and III, in 3D FRPC laminates where the crack impinges on the interface. Finally, the obtained framework is validated by two benchmark problems including the mode I and mode II delamination test, and is compared against experimental data reported in the literature.

A model for modifying the S‐N curve considering the effect of boundary conditions on the fatigue crack growth of welded components

AbstractThe present study proposes a novel model to modify master S‐N curves of components according to their load redistribution capability reflected in different boundary conditions (BCs) based on the fracture mechanics analysis. To that end, a comprehensive numerical study was conducted on a Single Edge Notch Bend (SENB) specimen constrained with different kinematic BCs using discrete fatigue crack growth (FCG) simulation. It was observed that BCs indeed can have a significant effect on the crack growth behavior and consequently on the resulting fatigue life under the same nominal loading conditions. The proposed model was applied to the S‐N curve of a T‐welded joint, and the predicted fatigue life was validated against 3D FCG simulations. Finally, FCG tests were conducted on SENB specimens to experimentally corroborate the effect of BCs on the FCG rate.

Multiple discrete crack initiation and propagation in Material Point Method

Cracks in MPM (CRAMP) is one of the most prominent discrete crack simulation methods in the Material Point Method (MPM) due to its simplicity and versatility. However, CRAMP is yet to include the capability to simulate concurrent crack initiations and propagations, as well as propagation to the edge of the material domain. The method proposed in this paper enables the simulation of multiple crack paths with CRAMP via the dynamic assignment of particles to separate grids while minimizing the number of necessary grids. It also proposes methods of evaluating crack initiation and propagation via the Rankine criterion. The proposed methods are then implemented in an in-house Convected Particle Domain Interpolation (CPDI) MPM developed at Aalto University.To verify the integrity of the CPDI algorithm, our CPDI code with the proposed method implemented simulated a CPDI vortex. Furthermore, six fracture-simulation verification test cases were carried out: (1) through-crack in an infinite plate; (2) mode-I propagation; (3) initiation; (4) initiation with large deformations; (5) merging; (6) multiple initial cracks; and (7) radially-cracked thick ring. All these verification tests show successful initiation, propagation, merging, crack opening, and agreement with the results from the literature, as well as the convergence of various parameters with the expected rates.

A Multi-Stage Feature Aggregation and Structure Awareness Network for Concrete Bridge Crack Detection.

One of the most significant problems affecting a concrete bridge's safety is cracks. However, detecting concrete bridge cracks is still challenging due to their slender nature, low contrast, and background interference. The existing convolutional methods with square kernels struggle to capture crack features effectively, fail to perceive the long-range dependencies between crack regions, and have weak suppression ability for background noises, leading to low detection precision of bridge cracks. To address this problem, a multi-stage feature aggregation and structure awareness network (MFSA-Net) for pixel-level concrete bridge crack detection is proposed in this paper. Specifically, in the coding stage, a structure-aware convolution block is proposed by combining square convolution with strip convolution to perceive the linear structure of concrete bridge cracks. Square convolution is used to capture detailed local information. In contrast, strip convolution is employed to interact with the local features to establish the long-range dependence relationship between discrete crack regions. Unlike the self-attention mechanism, strip convolution also suppresses background interference near crack regions. Meanwhile, the feature attention fusion block is presented for fusing features from the encoder and decoder at the same stage, which can sharpen the edges of concrete bridge cracks. In order to fully utilize the shallow detail features and deep semantic features, the features from different stages are aggregated to obtain fine-grained segmentation results. The proposed MFSA-Net was trained and evaluated on the publicly available concrete bridge crack dataset and achieved average results of 73.74%, 77.04%, 75.30%, and 60.48% for precision, recall, F1 score, and IoU, respectively, on three typical sub-datasets, thus showing optimal performance in comparison with other existing methods. MFSA-Net also gained optimal performance on two publicly available concrete pavement crack datasets, thereby indicating its adaptability to crack detection across diverse scenarios.

Uma abordagem direta pelo MEF para modelar concreto em mesoescala e conectar malhas não conformes em análises multiescala

Abstract The mechanical degradation of concrete structures is a phenomenon dependent on the material heterogeneity observed at mesoscale. As the mechanical degradation is a localized phenomenon, structural members and structures may be simulated using the concurrent multiscale analysis technique. Thus, only the most critical regions are modeled in mesoscale, reducing the computational cost compared to the simulation of the entire structure at this scale. This work presents two contributions in concurrent multiscale analysis. The first contribution introduces an alternative representation of the mesoscale interfacial transition zone (ITZ) of the concrete together with a strategy that allows modeling particles (coarse aggregates) without degrees of freedom. The resulting ITZ representation allows the simulation of more realistic discrete cracks in concrete modeling. The second contribution uses particle-like elements without degrees of freedom as coupling elements to model non-matching meshes between different media. The proposed coupling technique does not add degrees of freedom and does not use penalty or Lagrange Multipliers methods. Experimental and numerical results are used in order to validate the proposed multiscale formulation regarding concrete specimen simulations.