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The purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the extended finite element method (XFEM) approach. This provides a general and simple solution for the modeling of crack in the structure to analyze the repair.

The extended finite element method is used to model crack geometry. The crack surface is modeled by Heaviside enrichment function while the crack front is modeled by branch enrichment functions.

The effectiveness of the repair is measured in terms of stress intensity factor and J-integral. The critical voltage at which patch repair is most effective is evaluated and presented. Optimal patch shape, location of patch, adhesive thickness and adhesive modulus are obtained for effective repair under thermo-mechanical loading environment.

The presented numerical modeling and simulation by the XFEM approach are of great benefit to analyze crack repair in two-dimensional and three-dimensional structures using piezoelectric patch material under thermo-mechanical loading.

This study presents finite element (FE) and generalized regression neural network (GRNN) approaches for modeling multiple crack growth problems and predicting crack-growth directions under the influence of multiple crack parameters.

To determine the crack-growth direction in aluminum specimens, multiple crack parameters representing some degree of crack propagation complexity, including crack length, inclination angle, offset and distance, were examined. FE method models were developed for multiple crack growth simulations. To capture the complex relationships among multiple crack-growth variables, GRNN models were developed as nonlinear regression models. Six input variables and one output variable comprising 65 training and 20 test datasets were established.

The FE model could conveniently simulate the crack-growth directions. However, several multiple crack parameters could affect the simulation accuracy. The GRNN offers a reliable method for modeling the growth of multiple cracks. Using 76% of the total dataset, the NN model attained an R2 value of 0.985.

The models are presented for static multiple crack growth problems. No material anisotropy is observed.

In practical crack-growth analyses, the NN approach provides significant benefits and savings.

The proposed GRNN model is simple to develop and accurate. Its performance was superior to that of other NN models. This model is also suitable for modeling multiple crack growths with arbitrary geometries. The proposed GRNN model demonstrates its prediction capability with a simpler learning process, thus producing efficient multiple crack growth predictions and assessments.

This paper gives a bibliographical review of the finite element methods (FEMs) applied to the analysis of ceramics and glass materials. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1977‐1998. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, ferrites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.

This study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C¹ basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance measures, are used in the context of natural neighbor shape functions. The capability and efficiency of this method are studied for modeling cracks.

The weak form of the fourth-order PFM is derived from two governing equations for finite element modeling. C⁰ non-Sibsonian shape functions are derived using distance measures on a generalized quad element. Then these shape functions are degree elevated with Bernstein-Bezier (BB) patch to get higher-order continuity (C¹) in the shape function. The quad element is divided into several background triangular elements to apply the Gauss-quadrature rule for numerical integration. Both fourth-order and second-order PFMs are implemented in a finite element framework. The efficiency of the interpolation function is studied in terms of convergence and accuracy for capturing crack topology in the fourth-order PFM.

It is observed that fourth-order PFM has higher accuracy and convergence than second-order PFM using non-Sibsonian type interpolants. The former predicts higher failure loads and failure displacements compared to the second-order model due to the addition of higher-order terms in the energy equation. The fracture pattern is realistic when only the tensile part of the strain energy is taken for fracture evolution. The fracture pattern is also observed in the compressive region when both tensile and compressive energy for crack evolution are taken into account, which is unrealistic. Length scale has a certain specific effect on the failure load of the specimen.

Fourth-order PFM is implemented using C¹ non-Sibsonian type of shape functions. The derivation and implementation are carried out for both the second-order and fourth-order PFM. The length scale effect on both models is shown. The better accuracy and convergence rate of the fourth-order PFM over second-order PFM are studied using the current approach. The critical difference between the isotropic phase field and the hybrid phase field approach is also presented to showcase the importance of strain energy decomposition in PFM.

This paper describes progress on the development of theoretical models required for studying failure mechanism, crack initiation and growth around the boreholes driven by hydrofracturing processes in Hot Dry Rock (HDR) reservoirs of geothermal energy. Due to the importance of the stress intensity factor concept (K) in Fracture Mechanics, some advanced modeling techniques for accurate and fast determination of K for relevant problems are proposed. Alternative tools to deal with stress intensity factor determination are developed and assessed from the points of view of accuracy and computational cost. We concentrate on residual strength, crack initiation and crack growth as a means to model and understand experimentally observed behaviors. Several modeling methods such as compounding and weight function techniques, and boundary and finite element modeling for stress intensity factor calculation are discussed. Further to reviews of those techniques, work performed included (i) developing alternative solutions to deal with boundary‐to‐boundary interaction when using the compounding technique, (ii) relating the precision of K calculations with the level of precision of the crack opening displacement of a reference solution, in order to assess the precision of weight function technique, (iii) modeling relevant geometries using the finite element method (FEM), (iv) working on the implementation of direct stress intensity factor K determination in the Higher Order Displacement Discontinuity Method (HODDM), and (v) developing tools to deal with residual stress fields around the boundary of the hydraulically pressurized boreholes.

The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures.

The extended finite element method (XFEM) using four-node quadrilateral element associated with the fictitious cohesive crack model is used. A mixed-mode traction-separation law is assumed for the cohesive crack in the fracture process zone (FPZ). Enrichments are considered for both partly and fully cracked elements, and it thus makes the evolution of crack to any location inside the element possible. In all. two new solution procedures based on Newton-Raphson method, which differ from the approach suggested by Zi and Belytschko (2003), are presented to solve the nonlinear system of equations. The present formulation results in a symmetric tangent matrix, conveniently in finite element implementation and programming.

The inconvenience in solving the inversion of an unsymmetrical Jacobian matrix encountered in the existing approach is avoided. Numerical results evidently confirm the accuracy of the proposed approach. It is concluded that the developed XFEM approach is especially suitable in simulating cohesive crack growth in concrete structures.

Multiple cracks and crack growth in reinforced concretes should be considered in further studies.

The research paper presents a very useful and accurate numerical method for engineering application problems that has ability to numerically simulate the cohesive crack growth of concrete structures.

The research paper provides a new numerical approach using two new solution procedures in solving nonlinear system of equations for cohesive crack growth in concrete structures that is very convenient in programming and implementation.

The purpose of this paper is to present a simplified hybrid modeling (HYMOD) approach which overcomes limitations regarding computational cost and permits the simulation and prediction of the nonlinear inelastic behavior of full-scale RC structures.

The proposed HYMOD formulation was integrated in a research software ReConAn FEA and was numerically studied through the use of different numerical implementations. Then the method was used to model a full-scale two-storey RC building, in an attempt to demonstrate its numerical robustness and efficiency.

The numerical results performed demonstrate the advantages of the proposed hybrid numerical simulation for the prediction of the nonlinear ultimate limit state response of RC structures.

A new numerical modeling method based on finite element method is proposed for simulating accurately and with computational efficiency, the mechanical behavior of RC structures. Currently 3D detailed methods are used to model single structural members or small parts of RC structures. The proposed method overcomes the above constraints.

It has been usual to prefer an enrichment pattern independent of the mesh when applying singular functions in the Generalized/eXtended finite element method (G/XFEM). This choice, when modeling crack tip singularities through extrinsic enrichment, has been understood as the only way to surpass the typical poor convergence rate obtained with the finite element method (FEM), on uniform or quasi-uniform meshes conforming to the crack. Then, the purpose of this study is to revisit the topological enrichment strategy in the light of a higher-order continuity obtained with a smooth partition of unity (PoU). Aiming to verify the smoothness' impacts on the blending phenomenon, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU's with high-regularity.

The stress approximations right at the crack tip vicinity are qualified by focusing on crack severity parameters. For this purpose, the material forces method originated from the configurational mechanics is employed. Some attempts to improve solution using different polynomial enrichment schemes, besides the singular one, are discussed aiming to verify the transition/blending effects. A classical two-dimensional problem of the linear elastic fracture mechanics (LEFM) is solved, considering the pure mode I and the mixed-mode loadings.

The results reveal that, in the presence of smooth PoU's, the topological enrichment can still be considered as a suitable strategy for extrinsic enrichment. First, because such an enrichment pattern still can treat the crack independently of the mesh and deliver some advantage in terms of convergence rates, under certain conditions, when compared to the conventional FEM. Second, because the topological pattern demands fewer degrees of freedom and impacts conditioning less than the geometrical strategy.

Several outputs are presented, considering estimations for the J–integral and the angle of probable crack advance, this last computed from two different strategies to monitoring blending/transition effects, besides some comments about conditioning. Both h- and p-behaviors are displayed to allow a discussion from different points of view concerning the topological enrichment in smooth GFEM.

Reliable estimations of the extent of corrosion and time required to reach specific safety limits are crucial for assessing the reliability of aging reinforced concrete (RC) bridges. Engineers and decision-makers can use these figures to plan suitable inspection and maintenance operations.

Analytical, empirical and numerical approaches for estimating the service life of corroded RC structures were presented and compared. The concrete cover cracking times, which were predicted by the previously proposed analytical models, were compared with the experimentally obtained cracking times to identify the model/s for RC bridges. The shortcomings and limitations of the existing models are discussed.

The empirical models typically depend on the rate of corrosion, diameter of steel reinforcement and concrete cover depth and based on basic mathematical formula. In contrast, the analytical and numerical models contain the strength and stiffness properties of concrete as well as type of corrosion products and incorporate more complex mechanical factors. Four existing analytical models were analyzed and their performance was evaluated against existing experimental data in literature. All the considered analytical models were assumed thick-walled cylinder models. The maximum difference between observed cracking time from different test data and calculated cracking time using the developed models is 36.5%. The cracking times extend with increase in concrete cover and decrease with corrosion current density. The development of service life prediction models that considers factors such as heterogeneity of concrete, non-uniform corrosion along rebar, rust production rate and a more accurate representation of the corrosion accommodating region are some of the areas for further research.

Outcome of this paper partially bridge the gap between theory and practice, as it is the basis to estimate the serviceability of corrosion-affected RC structures and to propose maintenance and repair strategies for the structures. For structural design and evaluation, the crack-width criterion is the greatest practical importance, and structural engineers, operators and asset managers should pay close attention to it. Additionally, repair costs for corrosion-induced serviceability failures, particularly concrete cracking and spalling, are significantly higher than those for strength failures. Therefore, to optimize the maintenance cost of RC structures, it is essential to precisely forecast the serviceability of corrosion-affected concrete structures. The lifespan of RC structures may be extended by timely repairs. This helps stake holders to manage the resources.

In order to improve modeling of corrosion-induced cracking, important areas for future research were identified. Heterogeneity properties of concrete, concept of porous zone (accommodation effect of pores should be quantified), actual corrosion morphology (non-uniform corrosion along the length of rebar), interaction between sustain load and corrosions were not considered in existing models. Therefore, this work suggested for further researches should consider them as input and develop models which have best prediction capacity.

This work has positive impact on society and will not affect the quality of life. Predicting service life of structures is necessary for maintenance and repair strategy plans. Optimizing maintenance strategy is used to extend asset life, reduce asset failures, minimize repair cost, and improve health and safety for society.

The degree of accuracy and applicability of the existing service life prediction models used for RC were assessed by comparing the predicted cracking times with the experimentally obtained times reported in the literature. The shortcomings of the models were identified and areas where further research is required are recommended.

To provide a reinforced concrete model including bonding coupled to a classical continuum damage model of concrete, capable of predicting numerically the crack pattern distribution in a RC structure, subjected to traction forces.

A new coupling between bonding model and an alternative model for concrete cracking is proposed and analyzed. For concrete, proposes a damage‐like material model capable of combining two types of dissipative mechanisms: diffuse volume dissipation and localized surface dissipation.

One of the most important contributions is the capacity of predicting maximal and minimal spacing of macro‐cracks, even if the exact location of cracks remains undetermined. Another contribution is to reiterate on the insufficiency of the local damage model of concrete to handle this class of problems; much in the same manner as for localization problem which accompany strain‐softening behavior.

Bonding becomes very important to evaluate both the integrity and durability of a RC structure, or in particular to a reliable prediction of crack spacing and opening, and it should be integrated in future analysis of RC.

Shows that introduction of the influence of concrete heterogeneities in numerical analysis can directly affect the configuration of the crack pattern distribution. Use of a strong discontinuity approach provides additional cracking information like opening of macro‐cracks.