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This research delves into the fracture analysis of cellular thermosetting polymers using Mode I fracture tests with a compact tension geometry subjected to both monotonic and cyclic loadings. The equivalent linear elastic fracture mechanics concept effectively described crack initiation and propagation. Numerical simulations estimated the equivalent linear elastic crack length aligning with experimental measurements. Resistance curves revealed a transient regime followed by a self‐similar regime with relatively constant fracture energy, typical of quasi‐brittle materials. Finally, the fracture energy evolution correlated with macroscopic density evolution exhibiting a linear relationship relaying the influence of microstructure to a second order. [ABSTRACT FROM AUTHOR]

Oxide-graphite refractories represent the new paradigm of materials for extreme environments since 1970's: materials that resist thanks to "in situ" microstructural changes. The analysis of post-mortem linings necessitates the use of small specimens because main microstructural changes occur within the matrix, exhibiting zonal distributions relatively small compared to maximum aggregate sizes. In this paper the minimized tensile strength of discs (diameter = 18 mm, width = 8 mm) tested in diametral compression is addressed for commercial materials representative of the typical microstructures. Effects of aggregate and graphite sizes, graphite anisotropy and size of the specimens on the quasi-brittle fracture of these heterogeneous materials are discussed. [ABSTRACT FROM AUTHOR]

A brief review of crack path calculation methods using integral principles of mechanics is presented. In twodimensional setting, a crack is considered as a geodesic line on the surface of a body with a metric that depends on the initial stress state. The possibility of approximate determination of crack path on the basis of integral principles is illustrated on a number of problems. In particular, crack paths in a half-plane under uniformly distributed load applied on its edge are determined. The calculations include the stress state of the half-plane taken from the solution for a body without a crack. The fruitfulness of the representation of displacements of crack edges using the Winkler’s hypothesis is shown. To study the subcritical behavior of the crack, the concept of cracon, a quasi-particle simulating the motion of the crack tip, can be introduced. The problem of determining the crack path on the basis of integral principles of mechanics is insufficiently investigated and requires further research.

In this study, an improved discontinuous deformation analysis method with sub-block strategy is introduced to numerically simulate mixed-mode fractures. This approach partitions the material domain into continuum and potential discontinuum regions, applying specialized modeling techniques to each. In the continuum region, penalty-like bonding springs are employed to glue the sub-blocks together to capture the elastic behavior of the material. In the potential discontinuum region, the cohesive springs with the stiffness based on the cohesive zone model are implemented between sub-blocks to reproduce the process of crack nucleation and propagation. The primary advantage of this method is its capability to effectively model the transition of quasi-brittle solids from a continuous to a discontinuous stage through the degradation of cohesive springs. This accurately represents material failure while maintaining stability and consistency along uncracked interfaces. Another significant benefit is the method's efficiency, as it avoids complex contact operations along sub-block interfaces before the cohesive spring between them fails. Validation through various benchmark numerical examples, such as cantilever beam-bending and diverse fracture simulations, demonstrates the method's accuracy and robustness by comparing the results with analytical solutions. These comparisons show that the proposed method effectively captures the interplay between tensile and shear traction components in the mixed-mode crack propagation process. [ABSTRACT FROM AUTHOR]

The formation and development of cracks in samples made of ferromagnetic material, cast iron grade SCh 35, which are in a uniformly magnetized state under the influence of an internal magnetic field with a strength of more than 20 kA/m, has been studied. The anisotropic nature of quasi-brittle fracture and the magnitude of mechanical stresses at which fracture occurs are shown. Cracks propagating along magnetic field lines dominate. A possible reason for this is the magnetic interaction between the surfaces of the microcrack. [ABSTRACT FROM AUTHOR]

We present a refined engineering theory of cracks based on a two-parameter strength criterion. Unlike the basic theory, the refined approach utilizes an improved algorithm for the regular stress component computation. This improvement allows extending the engineering theory to longer cracks. The two-parameter Leonov–Panasyuk–Dugdale fracture criterion serves as a basis. A coupled fracture criterion includes a strain-based criterion, which is formulated at the tip of the true crack, as well as a stress-based criterion, formulated at the tip of the fictitious crack. Based on the refined criterion, quasi-brittle fracture curves are constructed for a compact specimen, a strip with an edge crack, and a four-point bending beam. To validate the new refined fracture criterion, we present simulation results of quasi-brittle fracture for structures made from various virtual materials. The corresponding virtual materials are modeled using a nonlocal damage theory accounting for the average size of the aggregate state of the material. Additionally, various classes of damage accumulation hypotheses are considered. Analysis of various types of virtual materials provides insights into the impact of hypotheses behind the engineering theory. For each type of material, the influence of the microstructural length scale on the overall structural strength is investigated. The analysis shows that the refined engineering theory has a wider range of applicability as compared to the basic theory based on two-parameter strength criteria. [ABSTRACT FROM AUTHOR]

Computational analysis of quasi-brittle fracture in cement-based and similar composites, supplied by various types of rod, fibre, etc. reinforcement, is crucial for the prediction of their load bearing ability and durability, but rather difficult because of the risk of initiation of zones of microscopic defects, followed by formation and propagation of a large number of macroscopic cracks. A reasonable and complete deterministic description of relevant physical processes is rarely available. Thus, due to significance of such materials in the design and construction of buildings, semi-heuristic computational models must be taken into consideration. These models generate mathematical problems, whose solvability is not transparent frequently, which limits the credibility of all results of ad hoc designed numerical simulations. In this short paper such phenomena are demonstrated on a simple model problem, covering both micro- and macro-cracking, with references to needful generalizations and more realistic computational settings. [ABSTRACT FROM AUTHOR]

The elastodynamic stress field near a crack tip propagating at a constant speed in isotropic quasi-brittle material was investigated, taking into account the strain gradient and inertia gradient effects. An asymptotic solution for a steady-state Mode-I crack was developed within the simplified strain gradient elasticity by using a representation of the general solution in terms of Lamé potentials in the moving framework. It was shown that the derived solution predicts the nonsingular stress state and smooth opening profile for the growing cracks that can be related to the presence of the fracture process zone in the micro-/nanostructured quasi-brittle materials. Note that similar asymptotic solutions have been derived previously only for Mode-III cracks (under antiplane shear loading). Thus, the aim of this study is to show the possibility of analytical assessments on the elastodynamic crack tip fields for in-plane loading within gradient theories. By using the derived solution, we also performed analysis of the angular distribution of stresses and tractions for the moderate speed of cracks. It was shown that the usage of the maximum principal stress criterion within second gradient elastodynamics allows us to describe a directional stability of Mode-I crack growth and an increase in the dynamic fracture toughness with the crack propagation speed that were observed in the experiments with quasi-brittle materials. Therefore, the possibility of the effective application of regularized solutions of strain gradient elasticity for the refined analysis of dynamic fracture processes in the quasi-brittle materials with phenomenological assessments on the cohesive zone effects is shown. [ABSTRACT FROM AUTHOR]

Carbon/glass fiber reinforced polymer composite panels may experience minor surface scratches during processing or use. These shallow scratches can expand and potentially lead to dangerous fracture failure as the specimens are continually loaded. This study presents a closed form non-LEFM model for predicting the fracture performance of materials with slight scratches. First, 3-p-b tests and direct tensile tests were conducted on 115 carbon/glass fiber composite laminated panel specimens. A comparison of the two test methods revealed that 3-p-b tests were more suitable for analyzing quasi-brittle fracture in carbon/glass fiber composites. The tensile strength f t and fracture toughness K I C of 3-p-b specimens with and without notched were discussed using the weighted average calculation method to determine the thickness of the "composite" single-layer prepreg as the characteristic composite unit C c h . A normal distribution method was also introduced to analyze the experimental discrete points, covering almost all the experimental scatterers with desired reliability. Furthermore, the same method was applied to specimens with different layup methods, and the data analysis confirmed its effectiveness. As the seam-thickness ratio α increases within a certain range, the tensile strength f t showed an overall increasing trend and the peak load P m a x showed a decreasing trend. Additionally, the laboratory routine dimensions can be utilized to efficiently predict the fracture of large size members with defects at the same thickness, which is significant for the safe design of composite structures. [ABSTRACT FROM AUTHOR]

The application of various methods of the theory of critical distances for evaluating the cleavage failure of a quasi-brittle plate with a notch in the form of a circular hole that is subjected to uniaxial tension, uniaxial compression, and also to the combined action of tensile and compressive stresses is considered. Critical stress calculations have been performed based on the previously proposed approach, according to which the structural parameter of the nonlocal failure criterion is represented as the sum of two terms. The first of them characterizes the actual structure of the material and is a constant, while the second one reflects the formation of inelastic deformations and depends on the plastic properties of the material, sample geometry, and boundary conditions. The calculation results are compared with known experimental data. [ABSTRACT FROM AUTHOR]

It is urgent to study the damage mechanism of corn kernels and find ways of reducing the rate of kernel breakage in mechanical threshing. This paper, by studying the mechanical curves and deformation characteristics of corn kernels with different moisture contents, points out the brittle mechanical characteristics of corn kernel damage fracture with low moisture content, and clarifies the variation law of mechanical properties of kernels with moisture contents. The experimental data of fatigue load - fatigue life curves of corn kernels with different moisture contents were described by the power function equation. At the same time, the fatigue life and damage characteristics of kernel with different moisture content were analyzed, and the accuracy of the fitting equation was verified. Through mathematical statistical analysis, the normal distribution curve of fatigue life was fitted, and the variation law of normal distribution curve with moisture content and fatigue load was determined. [ABSTRACT FROM AUTHOR]

In this work, we use computer simulation methods to study crack formation in the refractory lining of steel ladles when the molten metal is poured into a ladle. The aim was to determine thermal and mechanical conditions under which cracks might appear in the lining elements and to predict the direction and length of such cracks. Numerical studies were performed using finite and discrete element methods. Local fracture analysis was carried based on the criteria that take various elementary fracture mechanisms into account. Typical cases of the working lining layer functioning under different mechanical constraints and temperature conditions at the back face, which are determined by specific features of the buffer and heat-insulating lining layers, were considered. General patterns of crack initiation in different areas of lining elements under thermal shock caused by pouring the molten metal into the ladle are specified. The presence of a temperature gradient parallel to the hot face can lead to deviations in the crack trajectory mainly in the direction of the hot area of lining elements. [ABSTRACT FROM AUTHOR]

With the localizing gradient enhancement, a damage model for quasi-brittle materials is able to achieve regularized softening responses, with localized damage profiles corresponding to the development of macroscopic cracks, to resolve the numerical spurious effects induced by the conventional gradient enhancement. The typical implementation strategy for a gradient enhanced model is to solve the system of governing equations simultaneously. Focusing on the finite element (FE) package Abaqus, a user element subroutine is required to define the finite elements with additional degrees of freedom for the nonlocal field. Moreover, with user elements, additional effort is required to visualize the numerical results. To an inexperienced engineer/researcher, these requirements can be challenging. In this paper, a simple implementation of the localizing gradient damage model is elaborated. By utilizing the in-built coupled thermo-mechanical elements in Abaqus, the user only needs to define the material constitutive laws, as well as the sensitivity terms with respect to the field variables. Post-processing of results can be done directly in Abaqus. The applicability and ease of implementation are demonstrated via several examples, including those that utilize the Abaqus features of element deletion, contact between surfaces, as well as the incorporation of cohesive elements. Sample files can be downloaded from https://github.com/leonghien/Localizing-Gradient-Damage-with-UMAT-UMATHT [ABSTRACT FROM AUTHOR]

This study investigates the quasi-brittle fracture parameters of carbon fiber composites with shallow surface scratches by considering single-layer prepreg thickness as the characteristic composite microstructure. Three-point bending fracture tests were conducted on single-edge notched specimens of various-sized carbon fiber composites. The boundary effect model was employed to establish the relationship between the microstructure and macroscopic mechanical characteristics of carbon fiber composites. The maximum fracture load was used to determine the quasi-brittle fracture characteristics. By employing normal distribution analysis, the tensile strength and fracture toughness of each specimens were determined as f t = 453.28 MPa and K IC = 22.2 MPa √ m, respectively. The analysis results exhibited an error of only 0.39 % compared to the least-squares fit, and encompassed almost all discrete points of the specimens within a 95 % reliability range. Using standard laboratory dimensions, fracture intervals for different notched depths at the same thickness can be predicted. Furthermore, the fracture parameters demonstrated an increasing trend within a certain range as the crack-thickness ratio increases, which aligns with the theoretical findings. [ABSTRACT FROM AUTHOR]

A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities is studied with respect to its shape differentiability. The specific problem stemming from quasi-brittle fracture describes an elastic body with a Barenblatt cohesive crack under the inequality condition of non-penetration at the crack faces. Based on the Lagrange approach and using smooth penalization with the Lavrentiev regularization, a formula for the shape derivative is derived. The explicit formula contains both primal and adjoint states and is useful for finding descent directions for a gradient algorithm to identify an optimal crack shape from a boundary measurement. Numerical examples of destructive testing are presented in 2D. [ABSTRACT FROM AUTHOR]

In this study, an effective numerical framework for fracture simulations is proposed using the edge-based smoothed finite element method (ES-FEM) and isotropic damage model. The duality between the Delaunay triangulation and Voronoi tessellation is utilized for the mesh construction and the compatible use of the finite element solution with the Voronoi-cell lattice geometry. The mesh irregularity is introduced to avoid calculating the biased crack path by adding random variation in the nodal coordinates, and the ES-FEM elements are defined along the Delaunay edges. With the Voronoi tessellation, each nodal mass is calculated and the fractured surfaces are visualized along the Voronoi edges. The rotational degrees of freedom are implemented for each node by introducing the elemental formulation of the Voronoi-cell lattice model, and the accurate visualizations of the rotational motions in the Voronoi diagram are achieved. An isotropic damage model is newly incorporated into the ES-FEM formulation, and the equivalent elemental length is introduced with an additional geometric factor to simulate the consistent softening behaviors with reducing the mesh sensitivity. The full matrix form of the smoothed strain-displacement matrix is constructed for optimal use in the element-wise computations during explicit time integration, and parallel computing is implemented for the enhancement of the computational efficiency. The simulated results are compared with the theoretical solutions or experimental results, which demonstrates the effectiveness of the proposed methodology in the simulations of the quasi-brittle fractures. [ABSTRACT FROM AUTHOR]

The elastodynamic stress field near a crack tip propagating at a constant speed in isotropic quasi-brittle material was investigated, taking into account the strain gradient and inertia gradient effects. An asymptotic solution for a steady-state Mode-I crack was developed within the simplified strain gradient elasticity by using a representation of the general solution in terms of Lamé potentials in the moving framework. It was shown that the derived solution predicts the nonsingular stress state and smooth opening profile for the growing cracks that can be related to the presence of the fracture process zone in the micro-/nanostructured quasi-brittle materials. Note that similar asymptotic solutions have been derived previously only for Mode-III cracks (under antiplane shear loading). Thus, the aim of this study is to show the possibility of analytical assessments on the elastodynamic crack tip fields for in-plane loading within gradient theories. By using the derived solution, we also performed analysis of the angular distribution of stresses and tractions for the moderate speed of cracks. It was shown that the usage of the maximum principal stress criterion within second gradient elastodynamics allows us to describe a directional stability of Mode-I crack growth and an increase in the dynamic fracture toughness with the crack propagation speed that were observed in the experiments with quasi-brittle materials. Therefore, the possibility of the effective application of regularized solutions of strain gradient elasticity for the refined analysis of dynamic fracture processes in the quasi-brittle materials with phenomenological assessments on the cohesive zone effects is shown.

Abstract A comprehensive overview of state-of-the-art experimental, theoretical and numerical methods that aid understanding and predicting the quasi-brittle fracture behavior of plain concrete under quasi-static conditions is presented in this work. The main objectives of this paper are as follows: (a) to lay-out a systematic manner for experimental and modeling people to select their choice of a concrete fracture simulating tool, (b) to critically describe the advantages and disadvantages of conducting different experimental set-ups for researchers intending to perform their own experiments for model validation, and (c) to provide modelers with a one-stop-shop for experimental data on plain concrete. In this review paper, the general characteristics of crack propagation in concrete are also presented. Extensive literature on the experimental studies of mode I and mixed-mode quasi-brittle fracture in concrete is discussed. The two main features of numerical modeling of concrete fracture, which are the descriptions of strain-softening and nonlocal regularization, are reviewed, and the application of these features to the various damage models is discussed. The survey of numerical models covered in this paper range from continuum-based to discrete formulations. We also provide a critical discourse on the advantages and disadvantages of the discussed experimental and numerical tools used for studying and modeling concrete fracture, and this is succinctly presented in Tables 2 and 3, respectively. Finally, future considerations of the experimental, theoretical and numerical studies in concrete fracture are presented. [ABSTRACT FROM AUTHOR]

Phase field models have a very good capability in predicting the crack path, but most of them represent the dependence of the regularization parameter on the load‐carrying capacity of structures. In this paper, a phase field model is coupled with isotropic damage model aiming to resolve this issue in the fracture simulations of quasi‐brittle materials. Damage variables are calculated by a continuum damage mechanics model based on accurate energy reduction and then regularized by the phase field model. Since the continuum damage mechanics model is combined with phase field method, tensile strength of material is employed for calculating the damage field and phase field. Our approach can predict the accurate load‐carrying capacity independent of the regularization parameter while maintaining the precision of the crack path prediction. Three benchmark problems are solved to demonstrate good performance of our approach, and results are compared with those by the damage mechanics model or by the standard phase field model. [ABSTRACT FROM AUTHOR]

• Extension of meshless LPM method for simulating complex quasi-brittle fracture. • Various yield surfaces are incorporated in LPM for complex damage modelling. • Determination of characteristic length scale based on mode-I fracture is described. • Particle size independent solution can be obtained using the present method. In this paper, a local isotropic damage model is incorporated into the lattice particle method (LPM) to model complex quasi-brittle fracture problems. The issue of particle-size dependency is addressed using fracture energy in the damage model regularized with characteristic length that is particle-size dependent. The characteristic lengths are first estimated from mode-I fracture test by ensuring the prescribed and calculated fracture energies match well for both 2D and 3D cases. Extensive validation against experimental data in terms of crack path and structural response is then carried out to assess the accuracy of the proposed model in 2D and 3D settings. Positive outcomes, in line with the experimental findings, have been obtained for both 2D and 3D problems covering mode I and mixed-mode fractures. Furthermore, by employing a regular lattice network, the present model, when integrated with more sophisticated yield surfaces, can address intricate 3D fracture problems that entail the twisting of crack surfaces. Convergence of structural response and crack path is obtained when the particle spacing is refined. [ABSTRACT FROM AUTHOR]

Acoustic emission (AE) activity data resulting from the fracture processes of brittle materials is valuable real time information regarding the evolving state of damage in the material. Here, through a combined experimental and computational study we explore the possibility of utilising the statistical signatures of AE activity data for characterisation of disorder parameter in simulation of tensile fracture of epoxy based polymer. For simulations we use a square random spring network model with quasi-brittle spring behaviour and a normally distributed failure strain threshold. We show that the disorder characteristics while have marginal effect on the power law exponent of the avalanche size distribution, are strongly correlated with the waiting time interval between consecutive record breaking avalanches as well as the total number of records. This sensitivity to disorder is exploited in estimating the disorder parameter suitable for the experiments on tensile failure of epoxy based polymer. The disorder parameter is estimated assuming equivalence between the amplitude distribution of AE data and avalanche size distribution of the simulations. The chosen disorder parameter is shown to well reproduce the failure characteristics in terms of the peak load of the macroscopic response, the power-law behaviour with avalanche dominated fracture type as well as realistic fracture paths. • Computational fracture study using a quasi-brittle spring network model. • Strong correlation between extent of disorder and statistics of record avalanches. • Disorder parameter estimated from record statistics of experimental AE data. • Model reproduces characteristic features of experimental data. • Resolves challenge of disorder modelling in local fracture approach. [ABSTRACT FROM AUTHOR]

Abstract Crack initiation emerges due to a combination of elasticity, plasticity, and disorder, and it displays strong dependence on the material’s microstructural details. The characterization of the structural uncertainty in the original microstructure is typically empirical and systematic characterization protocols are lacking. In this paper, we propose an investigational tool in the form of the curvature of an ellipsoidal notch: As the radius of curvature at the notch increases, there is a dynamic phase transition from notch-induced crack initiation to disorder-induced crack nucleation. We argue that the this transition may unveil the characteristic length scale of structural disorder in the material. We investigate brittle but elastoplastic metals with continuum, microstructural disorder that could originate in a manufacturing process, such as alloying. We perform extensive and realistic simulations, using a phase-field approach coupled to crystal plasticity, where microstructural disorder and notch width are systematically varied. We identify the brittle-to-quasi-brittle transition for various disorder strengths in terms of the damage and stress evolution. Moreover, we investigate precursors to crack initiation that we quantify in terms of the expected stress drops during displacement control loading.

This paper presents the so‐called symmetric high‐order microplane (SYHOM) model for the simulation of damage localization and size effect in quasi‐brittle materials. Contrarily to its predecessor, the high order microplane (HOM) model, SYHOM is formulated without rotational degrees of freedom, does not require couple stresses, and solves stability issues created by the antisymmetric components of stress and high order stress tensors. Furthermore, the formulation features variable, damage‐dependent localization limiter and nonlocal characteristic length that allows reproducing correctly size and shape of the fracture process zone during the entire softening process: from crack initiation to the formation of a stress‐free fracture. The paper highlights the implementation of SYHOM via isogeometric analysis with quadratic shape functions and presents several numerical simulations to demonstrate SYHOM's ability to simulate damage evolution during softening. Finally, SYHOM is validated by simulating experimental data relevant to the size effect on structural strength of notched concrete samples. [ABSTRACT FROM AUTHOR]

The size effect of a quasi-brittle fracture is associated with the size of fracture process zone relative to the structural characteristic length. In numerical simulations using damage models, the nonlocal enhancement is commonly adopted to regularize the softening response. However, the conventional nonlocal enhancement, both integral and gradient approaches, induces a spurious spreading of damage zone. Since the evolution of fracture process zone cannot be captured well, the conventional nonlocal enhancement cannot predict the size effect phenomenon accurately. In this paper, the localizing gradient enhancement is adopted to avoid the spurious spreading of damage. Considering the three-point bend test of concrete beams, it is demonstrated that the dissipation profiles obtained with the localizing gradient enhancement compare well with those of reference meso-scale lattice models. With the correct damage evolution process, the localizing gradient enhancement is shown to capture the size effect phenomenon accurately for a series of geometrically similar concrete beams, using only a single set of material parameters. [ABSTRACT FROM AUTHOR]

The size effect of the strength of structurally inhomogeneous materials is manifested, in particular, in the dependence of the failure load on the size of the stress concentration zone that occurs near material or geometric inhomogeneities (inclusions, pores, cutouts, fillets). Although the size of the stress concentration zone is determined primarily by the size and shape of the inhomogeneity, the loading conditions also have a certain effect. In addition, the predictive value of the fracture theory is determined not only by the ability to take into account the size effect, but also by the possibility of extending the theory to the widest possible range of boundary conditions. The influence of boundary conditions and hole diameter on the initiation of tensile cracks at a circular hole in a quasi-brittle geomaterial under non-uniformly distributed compression was studied theoretically and experimentally, taking into account the scale factor. On the basis of the approach of the finite fracture mechanics, a criterion of quasi-brittle fracture is proposed. The results of calculating the critical stress are compared with the obtained experimental data. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, a general frictional cohesive zone model (FCZM) dedicated to quasi-brittle fracture is proposed to describe the mechanical response of an interface under combined traction or compression and shear loadings. Under combined traction and shear loadings, mixed-mode I + I I cohesive zone model, as proposed by Camanho et al. (2003), is used to express the mixed-mode response of the interface and the dependence to the loading path consistent to the one expected in quasi-brittle fracture. Under combined compression and shear loadings, the novelty lies in the proposed coupling between Mode II cohesive behavior and frictional behavior based on the damage level leading to a progressive rising of the frictional stress associated with the softening part of the cohesive behavior of the interface. FCZM thus describes a smooth transition from a cohesive zone to a pure frictional contact zone. Applied to the masonry context, this general FCZM can be fully characterized through two fracture tests carried out on small masonry assemblages. Finally, FCZM is implemented in LMGC90 discrete element code and used to simulate the experimental response of an unilateral cyclic shear test carried out on a triplet of limestone blocks assembled by two mortar joints. [ABSTRACT FROM AUTHOR]

Summary: Following the so‐called cracking elements method (CEM), we propose a novel Galerkin‐based numerical approach for simulating quasi‐brittle fracture, named global cracking elements method (GCEM). For this purpose the formulation of the original CEM is reorganized. The new approach is embedded in the standard framework of the Galerkin‐based finite‐element method (FEM), which uses disconnected element‐wise crack openings for capturing crack initiation and propagation. The similarity between the proposed global cracking elements (GCEs) and the standard nine‐node quadrilateral element (Q9) suggests a special procedure: the degrees of freedom of the center node of the Q9, originally defining the displacements, are "borrowed" to describe the crack openings of the GCE. The proposed approach does not need remeshing, enrichment, or a crack‐tracking strategy, and it avoids a precise description of the crack tip. Several benchmark tests provide evidence that the new approach inherits from the CEM most of the advantages. The numerical stability and robustness of the GCEM are better than the ones of the CEM. However, presently only quadrilateral elements with nonlinear interpolations of the displacement field can be used. [ABSTRACT FROM AUTHOR]

Copyright of Acta Materiae Compositae Sinica is the property of Acta Materiea Compositae Sinica Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study develops a hydro-damage-mechanical fully coupled numerical method capable of modelling complex fluid-driven transient dynamic crack propagation in quasi-brittle poroelastic media. In this method, the fluid flow in both fractures and porous media is described by a fluid continuity equation with the modified Darcy-Poiseuille law based on the Biot's poroelastic theory. The fluid pressure and the inertial force of solids are coupled by governing equations of the mesh-insensitive phase-field regularized cohesive zone model that can simulate quasi-brittle multi-crack initiation, propagation, branching and merging without remeshing or crack tracking. The resultant displacement-pressure-damage coupled multiphysics system of equations is solved using an alternative minimization Newton-Raphson iterative algorithm with an implicit Newmark integration scheme within the finite element framework. The new method was first validated by a few 2D problems, including crack branching and deflecting in solids, fracking in a concrete cube, and consolidation and stress wave propagation in poroelastic media, subjected to various impulsive loadings. It was then applied to pressure pulsing fracking of a 40 m granite rock reservoir with extensive parametric studies of fluid viscosity and pulsing injection rate, mode and period. It was found that pulsing injection with higher fluid rates and lower fluid viscosities resulted in more developed crack patterns, and in particular, there existed an optimal pulsing injection period that could promote fracking under relatively low injection pressures. 3D horizontal well problems with multiple non-planar crack propagation and bifurcation were also successfully simulated to demonstrate the capacity and potential of the new method for engineering design and optimization of pressure pulsing fracking. • A new hydromechanical coupled cohesive phase field method is developed for dynamic pulsing fracking for the first time. • The method can robustly and effectively simulate complex 2D/3D dynamic propagation and bifurcation of multiple hydrocracks. • It provides a promising tool for the design and optimization of pulsing fracking for fuel and energy exploitation. [ABSTRACT FROM AUTHOR]

• Propose an arbitrary polygon-based CSFEM-PFCZM to investigate quasi-brittle fracture of concrete-like materials. • Successfully simulate macroscale and mesoscale heterogeneous problems. • Show evident flexibility and efficiency over traditional FEM-PFCZM. • Hold promise to increase the acceptance and momentum of both the CSFEM and PFCZM in the research communities. In recent years, engineering and research communities have shown a growing interest in polygon elements due to their adaptability to complex geometries. However, their applicability for investigating the quasi-brittle damage and fracture of concrete structures is still an open question. This work thus develops a numerical framework to integrate the phase-field regularized cohesive zone model (PFCZM) with the cell-based smoothed finite element method (CSFEM) using arbitrary polygon elements. The techniques of centroidal Voronoi tessellation and polytree decomposition are adopted to discretize the computational domains and efficiently refine the potential cracking areas in a multi-level manner. This allows fast transition of the mesh density and direct elimination of the hanging-node issue using the CSFEM. To calculate the displacements and the damage variables, only Wachspress shape functions and boundary geometries are needed, eliminating the need for coordinate mapping and Jacobian inversion. For each CSFEM subcell, crack-driving forces are determined at the integration point and stored as history variables. Typical concrete structures under different loading conditions are validated with respect to the crack path and load-carrying capacity, exhibiting good coarse-mesh accuracy. A mesoscale test-piece under uniaxial tension is also modelled using the developed framework, showing significant computational efficiency when compared to the conventional FEM. [ABSTRACT FROM AUTHOR]

One of the long-standing problems in continuum damage mechanics is accurate prediction of damage evolution that accounts for the distribution of microstructural features. This is particularly true for microcracking solids, such as concrete, where non-uniformity in the size and spatial distribution of defects can lead to non-uniqueness in the continuum-averaged energy release rate (and free surface area creation) for cases where local microcrack growth occurs. In this work, a novel theoretical framework for quantifying the crack free surface area creation is formulated and used along with a previously developed non-local numerical technique known as Graph-based Finite Element Analysis (GraFEA). Using the 2D GraFEA approach and its implementation into a finite element code, the invariance of the crack free surface area created and the total amount of energy dissipated due to fracture was demonstrated. This research aims to honor the lifelong accomplishments of Professor Alan Needleman in computational modeling of deformation and fracture. • 2D GraFEA extended to estimate free surface area creation in microcracking concrete. • Used a non-local, stochastic model with population dynamics and survival probability. • Calibrated non-local characteristic length for concrete to estimate fracture energy. • Calculated fracture energy absorbed in concrete quasi-static boundary value problems. • This approach eliminated non-uniqueness in free surface area creation in GraFEA. [ABSTRACT FROM AUTHOR]

This paper is devoted to numerical investigation of quasi-brittle fracture under thermal-elastic loading condition using a novel thermal-mechanical local damage model associated with the enhanced bi-energy norm based equivalent strain. In contrast to the non-local or gradient-enhanced damage models, a local damage counterpart generally requires less computational effort. The common mesh-dependent issue encountered in the local approaches is here mitigated by incorporation of fracture energy and element characteristic length into the calculation of damage evolution. Equivalent strain is derived based on the so-called bi-energy norm concept and the recent Mazars' criterion. Here, the damage evolution is induced by both the mechanical and thermal loads, in which both stress and thermal conductance capacity are reduced across the damage zone. In this work, we present an efficient staggered scheme to solve the coupled thermal-mechanical damage equations. The performance and accuracy of the developed model are validated via several numerical examples of quasi-static crack growth problems, in which comparisons between the computed results and reference solutions from other numerical approaches and/or experiments are presented. [ABSTRACT FROM AUTHOR]

The influence of hole diameter on the fracture of quasi-brittle geomaterial in the stress concentration zone under non-uniformly distributed compression has been studied theoretically and experimentally taking into account the size effect. The failure load is determined using modified nonlocal criteria derived from the average stress criterion, the point stress criterion, and the fictitious crack criterion and containing a. complex parameter that characterizes the size of the fracture process zone and takes into account not only the material structure, but also the plastic properties of the material, the geometry of the sample, and loading conditions. The calculation results are compared with experimental data. [ABSTRACT FROM AUTHOR]

The paper analyzes the applicability of available nonlocal and gradient fracture criteria to brittle, quasi-brittle, and ductile fracture in notched materials. All chosen criteria use an internal size parameter as a material structure characteristic, which makes it possible to describe the scale effect under stress concentration and to extend the range of their application compared to conventional ones. However, this range is limited to brittle or quasi-brittle fracture with a small prefracture zone. For extending the criteria to quasi-brittle fracture with a developed prefracture zone, we should dismiss the hypothesis on the prefracture zone size as a constant related solely to the structure of materials. In this paper, a new physically substantiated approach is proposed which modifies the criteria of average stress, point stress, fictitious crack, and stress gradient such that their modified versions contain a complex parameter allowing for the size of a prefracture zone, structure of a material, its plastic properties, geometry, and loading conditions. Their experimental verification as applied to tensile cracking in compressed geomaterials with a round hole shows that all modified criteria provide a good description of quasi-brittle fracture and allow one to explain the experimentally observed transition from brittle to ductile fracture with increasing hole sizes. [ABSTRACT FROM AUTHOR]

Under impacts, monolithic quasi-brittle specimens fail by cracking if the magnitude of the induced stress waves exceeds their tensile strength. In spall tests, depending on the velocity of the striker hitting the specimen, either a partial damage or a whole crack formation can be induced. Since cracking occurs almost instantaneously in this dynamic process, experimental data need to be accurately and reliably filtered to identify the material strength and toughness ruling a cohesive law that describes the damaging/cracking event. To this aim, a Sigma-point Kalman filter approach is here discussed. The performance of the proposed methodology, in terms of constitutive parameter estimation and tracked specimen state, especially crack opening, is first quantitatively assessed through pseudo-experimental testing. It is shown that, if the stress pulse leads to a complete failure of the specimen and if the out-of-plane velocity is measured at the back surface of the impacted specimen, a noteworthy accurate and (almost) initialization-independent calibration of the cohesive model is obtained. Next, some results are provided by processing real experimental data relevant to two ceramic materials: SiC and B C. [ABSTRACT FROM AUTHOR]

Concrete, with its heterogeneous internal structure of cement mortar and grains, exhibits complex quasi-brittle cracking where a gradual decrease in the material integrity is observed. In practical engineering, concrete structures are commonly under loading conditions that cause complex mixed mode fracture patterns. Hence, the prediction of failure mechanisms and patterns in concrete is a demanding task. In the past decades, computational fracture modeling of concrete has proven to be a suitable substitute for costly experimental testing. Among many fracture models, the phase field approach, owing to its ability to capture various crack phenomena without a need for ad hoc criteria, has gained significant attention. Although there exist phase field models applied to various failure mechanisms ranging from brittle to ductile fractures, only a limited number of them deal with the quasi-brittle cracking observed in concrete. Hence, in this work, a thermodynamically consistent phase field approach for quasi-brittle fracture is presented, and its performance for capturing the mixed mode failure patterns of concrete is investigated. Starting from a purely geometric approach, the evolution of fracture is associated with a constitutive crack driving functional. The crack driving force is related to an equivalent effective stress measure leading to a simple, yet versatile, framework in which various failure criteria can be implicitly incorporated into the framework. In particular, equivalent effective stresses based on the Rankine, Drucker–Prager, modified von Mises, and three-parameter failure criteria are derived. A unified form of the equivalent effective stress encompassing all the models is also proposed, which offers flexibility in choosing an appropriate driving force, and allows a simple implementation into a finite element framework. Utilizing this unified form, the effectiveness of the aforementioned driving forces in capturing complex mixed mode cracking in concrete is investigated by comparing the results obtained from computational simulations to existing experimental data. In particular, the load–displacement curves and the crack propagation paths are compared with the corresponding experimental observations, and a systematic study of the performance of different driving forces is detailed in this study. [ABSTRACT FROM AUTHOR]

An analysis focused on capturing the phenomenon of quasi-brittle fracture is presented. Selected parameters relevant for quasi-brittle fracture are evaluated and an assessment of their dependence on the size and shape of the test specimen is studied. Determination of these fracture characteristics is based on the records of the fracture tests on notched specimens, particularly from recorded loading diagrams. A method of separation of the energy amounts released for the propagation of the (effective) crack and that dissipated within the volume of a large nonlinear zone at the crack tip – the fracture process zone – is introduced and tested on selected data from experimental campaigns published in the literature. The work is accompanied with own conducted numerical simulations using commercial finite element code with implemented cohesive crack model. Results from three-point bending tests on specimens of different sizes and relative notch lengths are taken into account in this study. The proposed model has only two parameters whose values are constant for all specimen sizes and notch lengths.

Highlights • Phase-field regularized CZM and GED models for cohesive fracture are compared. • PF-CZM converges to a discrete CZM, is mesh and length scale independent. • GED is mesh independent but length scale dependent. It suffers from damage widening. • Stress based GED removed drawbacks of GED but is not completely mesh insensitive. • PFM has an exponential crack like damage distribution whereas GED yields a bell like damage profile. • PF-CZM is more computationally intensive than GED/SB-GED. Abstract This paper presents a comparative study of the gradient-enhanced damage models (GED) of Peerlings et al. (1996), Vandoren and Simone (2018) and the phase field damage/fracture model (PFM) of Wu (2017), Wu and Nguyen (2018) within the context of the computational modeling of the fracture of quasi-brittle materials (concrete, ceramic, rock, ice, etc.). Being continuous damage/fracture models, these two models enjoy the simplicity of modeling the fracture process on a fixed finite element mesh. The similarities and differences of the two models are discussed by examining governing equations and conducting numerical simulations of some mode I and mixed-mode fracture benchmark tests. The most worthy findings are: (i) both classes of models can handle the initiation and propagation of cohesive cracks, (ii) they are totally different–PFM behaves like a cohesive zone model (a sub-class of fracture mechanics) when the length scale is sufficiently small and the response is insensitive to this length scale whereas GED is a non-local damage model (a sub-class of continuum damage mechanics) of which response obviously depends on the length scale. [ABSTRACT FROM AUTHOR]