Special Issue "Computational Methods for Fracture"

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (31 January 2019)

Special Issue Editor

Guest Editor
Prof. Dr.-Ing. Timon Rabczuk

Institut für Strukturmechanik, Bauhaus University Weimar, Marienstrasse 15, 99423 Weimar, Germany
Website | E-Mail
Phone: +1-419-530-8245
Interests: Constitutive Modeling; Material Instabilities, Fracture, Strain Localization; Numerical Methods (Extended Finite Element and Mesfhree Methods); Isogeometric Analysis; Computational Fluid-Structure Interaction; Biomechanical Engineering

Special Issue Information

Dear Colleagues,

Computational modeling of fracture and failure of engineering systems and materials has been the focus of research for many years, and there has been tremendous advancement in the past two decades with methods such as the Extended Finite Element Method (XFEM) developed in 1999, peridynamics (2000), the cracking particles method (2004) or phase field models (2009). There has been also a great deal of effort in developing multiscale methods for the design of new materials, such as the Extended Bridging Domain Method or the MAD method.

The main focus of this Special Issue is on computational methods for fracture. However, articles submitted to this Special Issue about validation, uncertainty quantification, large-scale engineering applications and constitutive modeling are also welcome. Potential topics include, but are not limited to:

  • New computational methods for fracture
  • Advances in partition of unity methods
  • Meshfree methods
  • Isogeometric analysis
  • Efficient remeshing techniques
  • Phase-field and screened-Poisson models for fracture
  • Peridynamics
  • Multiphysics problems such as hydraulic fracturing
  • Computational methods for crack detection
  • Large-scale engineering applications
  • Multiscale methods for fracture
  • Validation and uncertainty quantification

Prof. Dr. Timon Rabczuk
Guest Editor

Manuscript Submission Information

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Keywords

  • Fracture
  • Modeling and Simulation
  • Validation
  • Uncertainty Quantification
  • Finite Elements
  • Meshfree Methods
  • Peridynamics
  • Isogeometric Analysis

Published Papers (12 papers)

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Research

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Open AccessArticle Grouting Process Simulation Based on 3D Fracture Network Considering Fluid–Structure Interaction
Appl. Sci. 2019, 9(4), 667; https://doi.org/10.3390/app9040667 (registering DOI)
Received: 29 January 2019 / Revised: 11 February 2019 / Accepted: 12 February 2019 / Published: 15 February 2019
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Abstract
Grouting has always been the main engineering measure of ground improvement and foundation remediation of hydraulic structures. Due to complex geological conditions and the interactions between the grout and the fractured rock mass, which poses a serious challenge to the grouting diffusion mechanism [...] Read more.
Grouting has always been the main engineering measure of ground improvement and foundation remediation of hydraulic structures. Due to complex geological conditions and the interactions between the grout and the fractured rock mass, which poses a serious challenge to the grouting diffusion mechanism analysis, fracture grouting has been a research hotspot for a long time. In order to throw light on the grout diffusion process in the fractured rock mass and the influence of grout on the fracture network, and to achieve more realistic grouting numerical simulation, in this paper a grouting process simulation approach considering fluid–structure interaction is developed based on the 3D fractured network model. Firstly, the relationship between fracture apertures and trace lengths is used to obtain a more realistic value of fracture aperture; then a more reliable model is established; subsequently, based on the 3D fracture network model, different numerical models are established to calculate fluid dynamics (grout) and structure deformation (fractured rock mass), and the results are exchanged at the fluid–structure interface to realize the grouting process simulation using two-way fluid-structure interaction method. Finally, the approach is applied to analyze the grouting performance of a hydropower station X, and the results show that the grouting simulation considering fluid–structure interaction are more realistic and can simultaneously reveal the diffusion of grout and the deformation of fracture, which indicates that it is necessary to consider the effect of fluid–structure interaction in grouting simulation. The results can provide more valuable information for grouting construction. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle Long-Term Behaviour of Precast Concrete Deck Using Longitudinal Prestressed Tendons in Composite I-Girder Bridges
Appl. Sci. 2018, 8(12), 2598; https://doi.org/10.3390/app8122598
Received: 12 November 2018 / Revised: 4 December 2018 / Accepted: 5 December 2018 / Published: 13 December 2018
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Abstract
Twin-I girder bridge systems composite with precast concrete deck have advantages including construction simplification and improved concrete strength compared with traditional multi-I girder bridge systems with cast-in-place concrete deck. But the cracking is still a big issue at interior support for continuous span [...] Read more.
Twin-I girder bridge systems composite with precast concrete deck have advantages including construction simplification and improved concrete strength compared with traditional multi-I girder bridge systems with cast-in-place concrete deck. But the cracking is still a big issue at interior support for continuous span bridges using twin-I girders. To reduce cracks occurrence in the hogging regions subject to negative moments and to guarantee the durability of bridges, the most essential way is to reduce the tensile stress of concrete deck within the hogging regions. In this paper, the prestressed tendons are arranged to prestress the precast concrete deck before it is connected with the steel girders. In this way, the initial compressive stress induced by the prestressed tendons in the concrete deck within the hogging region is much higher than that in regular concrete deck without prestressed tendons. A finite element analysis is developed to study the long-term behaviour of prestressed concrete deck for a twin-I girder bridge. The results show that the prestressed tendons induce large compressive stresses in the concrete deck but the compressive stresses are reduced due to concrete creep. The final compressive stresses in the concrete deck are about half of the initial compressive stresses. Additionally, parametric study is conducted to find the effect to the long-term behaviour of concrete deck including girder depth, deck size, prestressing stress and additional imposed load. The results show that the prestressing compressive stress in precast concrete deck is transferred to steel girders due to concrete creep. The prestressed forces transfer between the concrete deck and steel girder cause the loss of compressive stresses in precast concrete deck. The prestressed tendons can introduce some compressive stress in the concrete deck to overcome the tensile stress induced by the live load but the force transfer due to concrete creep needs be considered. The concrete creep makes the compressive stress loss and the force redistribution in the hogging regions, which should be considered in the design the twin-I girder bridge composite with prestressed precast concrete deck. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle Cracking Risk and Overall Stability Analysis of Xulong High Arch Dam: A Case Study
Appl. Sci. 2018, 8(12), 2555; https://doi.org/10.3390/app8122555
Received: 31 October 2018 / Revised: 28 November 2018 / Accepted: 3 December 2018 / Published: 10 December 2018
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Abstract
It is of great significance to study the cracking risk, the overall stability, and the reinforcement measures of arch dams for ensuring long-term safety. In this study, the cracking types and factors of arch dams are summarized. By employing a nonlinear constitutive model [...] Read more.
It is of great significance to study the cracking risk, the overall stability, and the reinforcement measures of arch dams for ensuring long-term safety. In this study, the cracking types and factors of arch dams are summarized. By employing a nonlinear constitutive model relating to the yielding region, a fine three-dimensional finite element simulation of the Xulong arch dam is conducted. The results show that the dam cracking risk is localized around the outlets, the dam heel, and the left abutment. Five dam stress zones are proposed to analysis dam cracking state base of numerical results. It is recommended to use a shearing-resistance wall in the fault f57, replace the biotite enrichment zone with concrete and perform consolidation grouting or anchoring on the excavated exposed weak structural zone. Three safety factors of the Xulong arch dam are obtained, K_1 = 2~2.5; K_2 = 5; K_3 = 8.5, and the overall stability of the Xulong arch dam is guaranteed. This study demonstrates the significance of the cracking control of similar high arch dams. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle Three Dimensional CS-FEM Phase-Field Modeling Technique for Brittle Fracture in Elastic Solids
Appl. Sci. 2018, 8(12), 2488; https://doi.org/10.3390/app8122488
Received: 30 October 2018 / Revised: 22 November 2018 / Accepted: 22 November 2018 / Published: 4 December 2018
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Abstract
The cell based smoothed finite element method (CS-FEM) was integrated with the phase-field technique to model brittle fracture in 3D elastic solids. The CS-FEM was used to model the mechanics behavior and the phase-field method was used for diffuse fracture modeling technique where [...] Read more.
The cell based smoothed finite element method (CS-FEM) was integrated with the phase-field technique to model brittle fracture in 3D elastic solids. The CS-FEM was used to model the mechanics behavior and the phase-field method was used for diffuse fracture modeling technique where the damage in a system was quantified by a scalar variable. The integrated CS-FEM phase-field approach provides an efficient technique to model complex crack topologies in three dimensions. The detailed formulation of our combined method is provided. It was implemented in the commercial software ABAQUS using its user-element (UEL) and user-material (UMAT) subroutines. The coupled system of equations were solved in a staggered fashion using the in-built non-linear Newton–Raphson solver in ABAQUS. Eight node hexahedral (H8) elements with eight smoothing domains were coded in CS-FEM. Several representative numerical examples are presented to demonstrate the capability of the method. We also discuss some of its limitations. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle Progressive Collapse Analysis of SRC Frame-RC Core Tube Hybrid Structure
Appl. Sci. 2018, 8(11), 2316; https://doi.org/10.3390/app8112316
Received: 25 October 2018 / Revised: 13 November 2018 / Accepted: 15 November 2018 / Published: 20 November 2018
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Abstract
Steel reinforced concrete (SRC) frame-reinforced concrete (RC) core tube hybrid structures are widely used in high-rise buildings. Focusing on the progressive collapse behavior of this structural system, this paper presents an experiment and analysis on a 1/5 scaled, 10-story SRC frame-RC core tube [...] Read more.
Steel reinforced concrete (SRC) frame-reinforced concrete (RC) core tube hybrid structures are widely used in high-rise buildings. Focusing on the progressive collapse behavior of this structural system, this paper presents an experiment and analysis on a 1/5 scaled, 10-story SRC frame-RC core tube structural model. The finite element (FE) model developed for the purpose of progressive collapse analysis was validated by comparing the test results and simulation results. The alternate load path method (APM) was applied in conducting nonlinear static and dynamic analyses, in which key components including columns and shear walls were removed. The stress state of the beams adjacent to the removed component, the structural behavior including inter-story drift ratio and shear distribution between frame and tube were investigated. The demand capacity ratio (DCR) was applied to evaluate the progressive collapse resistance under loss of key components scenarios. The results indicate that the frame and the tube cooperate in a certain way to resist progressive collapse. The core tube plays a role as the first line of defense against progressive collapse, and the frame plays a role as the second line of defense against progressive collapse. It is also found that the shear distribution is related to the location of the component removed, especially the corner column and shear walls. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle Peridynamic Analysis of Rail Squats
Appl. Sci. 2018, 8(11), 2299; https://doi.org/10.3390/app8112299
Received: 18 October 2018 / Revised: 13 November 2018 / Accepted: 14 November 2018 / Published: 19 November 2018
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Abstract
Rail surface defects are a serious concern for railway infrastructure managers all around the world. They lead to poor ride quality due to excess vibration and noise; in rare cases, they can result in a broken rail and a train derailment. Defects are [...] Read more.
Rail surface defects are a serious concern for railway infrastructure managers all around the world. They lead to poor ride quality due to excess vibration and noise; in rare cases, they can result in a broken rail and a train derailment. Defects are typically classified as ‘rail studs’ when they initiate from the white etching layer, and ‘rail squats’ when they initiate from rolling contact fatigue. This paper presents a novel investigation into rail squat initiation and growth simulations using peridynamic theory. To the best of the authors’ knowledge, no other comprehensive study of rail squats has been carried out using this approach. Peridynamics are well-suited for fracture problems, because, contrary to continuum mechanics, they do not use partial-differential equations. Instead, peridynamics use integral equations that are defined even when discontinuities (cracks, etc.) are present in the displacement field. In this study, a novel application of peridynamics to rail squats is verified against a finite element solution, and the obtained simulation results are compared with in situ rail squat measurements. Some new insights can be drawn from the results. The outcome exhibits that the simulated cracks initiate and grow unsymmetrically, as expected and reported in the field. Based on this new insight, it is apparent that peridynamic modelling is well-applicable to fatigue crack modeling in rails. Surprisingly, limitations to the peridynamic analysis code have also been discovered. Future work requires finding an adequate solution to the matter-interpenetration problem. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle 2D Micromechanical Modeling and Simulation of Ta-Particles Reinforced Bulk Metallic Glass Matrix Composite
Appl. Sci. 2018, 8(11), 2192; https://doi.org/10.3390/app8112192
Received: 29 September 2018 / Revised: 2 November 2018 / Accepted: 5 November 2018 / Published: 8 November 2018
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Abstract
The influence of particle shape, orientation, and volume fractions, as well as loading conditions, on the mechanical behavior of Ta particles reinforced with bulk metallic glass matrix composite is investigated in this work. A Matlab program is developed to output the MSC.Patran Command [...] Read more.
The influence of particle shape, orientation, and volume fractions, as well as loading conditions, on the mechanical behavior of Ta particles reinforced with bulk metallic glass matrix composite is investigated in this work. A Matlab program is developed to output the MSC.Patran Command Language (PCL) in order to generate automatically two-dimensional (2D) micromechanical finite element (FE) models, in which particle shapes, locations, orientations, and dimensions are determined through a few random number generators. With the help of the user-defined material subroutine (UMAT) in ABAQUS, an implicit numerical method based on the free volume model has been implemented to describe the mechanical response of bulk metallic glass. A series of computational experiments are performed to study the influence of particle shapes, orientations, volume fractions, and loading conditions of the representative volume cell (RVC) on its composite mechanical properties. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle Numerical Analysis of a Moderate Fire inside a Segment of a Subway Station
Appl. Sci. 2018, 8(11), 2116; https://doi.org/10.3390/app8112116
Received: 25 September 2018 / Revised: 24 October 2018 / Accepted: 26 October 2018 / Published: 1 November 2018
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Abstract
A 1:4 scaled fire test of a segment of a subway station is analyzed by means of three-dimensional Finite Element simulations. The first 30 min of the test are considered to be representative of a moderate fire. Numerical sensitivity analyses are performed. As [...] Read more.
A 1:4 scaled fire test of a segment of a subway station is analyzed by means of three-dimensional Finite Element simulations. The first 30 min of the test are considered to be representative of a moderate fire. Numerical sensitivity analyses are performed. As regards the thermal boundary conditions, a spatially uniform surface temperature history and three different piecewise uniform surface temperature histories are used. As regards the material behavior of concrete, a temperature-independent linear-elastic model and a temperature-dependent elasto-plastic model are used. Heat transfer within the reinforced concrete structure is simulated first. The computed temperature evolutions serve as input for thermomechanical simulations of the fire test. Numerical results are compared with experimental measurements. It is concluded that three sources of uncertainties render the numerical simulation of fire tests challenging: possible damage of the structure prior to testing, the actual distribution of the surface temperature during the test and the time-dependent high-temperature behavior of concrete. In addition, the simulations underline that even a moderate fire represents a severe load case, threatening the integrity of the reinforced concrete structure. Tensile cracking is likely to happen at the inaccessible outer surface of the underground structure. Thus, careful inspection is recommended even after non-catastrophic fires. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle A Nonlinear Crack Model for Concrete Structure Based on an Extended Scaled Boundary Finite Element Method
Appl. Sci. 2018, 8(7), 1067; https://doi.org/10.3390/app8071067
Received: 27 April 2018 / Revised: 26 June 2018 / Accepted: 26 June 2018 / Published: 29 June 2018
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Abstract
Fracture mechanics is one of the most important approaches to structural safety analysis. Modeling the fracture process zone (FPZ) is critical to understand the nonlinear cracking behavior of heterogeneous quasi-brittle materials such as concrete. In this work, a nonlinear extended scaled boundary finite [...] Read more.
Fracture mechanics is one of the most important approaches to structural safety analysis. Modeling the fracture process zone (FPZ) is critical to understand the nonlinear cracking behavior of heterogeneous quasi-brittle materials such as concrete. In this work, a nonlinear extended scaled boundary finite element method (X-SBFEM) was developed incorporating the cohesive fracture behavior of concrete. This newly developed model consists of an iterative procedure to accurately model the traction distribution within the FPZ accounting for the cohesive interactions between crack surfaces. Numerical validations were conducted on both of the concrete beam and dam structures with various loading conditions. The results show that the proposed nonlinear X-SBFEM is capable of modeling the nonlinear fracture propagation process considering the effect of cohesive interactions, thereby yielding higher precisions than the linear X-SBFEM approach. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle Evaluation of the Implicit Gradient-Enhanced Regularization of a Damage-Plasticity Rock Model
Appl. Sci. 2018, 8(6), 1004; https://doi.org/10.3390/app8061004
Received: 11 May 2018 / Revised: 28 May 2018 / Accepted: 29 May 2018 / Published: 20 June 2018
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Abstract
In the present publication, the performance of an implicit gradient-enhanced damage-plasticity model is evaluated with special focus on the prediction of complex failure modes such as shear failure. Hence, it complements studies on predominant mode I failure frequently found in the literature. To [...] Read more.
In the present publication, the performance of an implicit gradient-enhanced damage-plasticity model is evaluated with special focus on the prediction of complex failure modes such as shear failure. Hence, it complements studies on predominant mode I failure frequently found in the literature. To this end, an implicit gradient-enhanced damage-plasticity rock model is presented and validated by means of 2D and 3D finite element simulations of both laboratory tests on intact rock specimens as well as a large-scale structural benchmark related to failure of rock mass. Thereby, a wide range of loading conditions comprising unconfined and/or confined, tensile and/or compressive stress states is considered. The capability of the gradient-enhanced rock model for representing the mechanical response objectively with respect to the finite element discretization and realistically compared to measurement data is assessed. It is shown that complex failure modes and the respective load–displacement curves are predicted in a mesh-insensitive manner. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Open AccessArticle A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation
Appl. Sci. 2018, 8(6), 975; https://doi.org/10.3390/app8060975
Received: 11 May 2018 / Revised: 9 June 2018 / Accepted: 12 June 2018 / Published: 14 June 2018
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Abstract
The High-order Shear Deformation Theories (HSDTs) which can avoid the use of a shear correction factor and better predict the shear behavior of plates have gained extensive recognition and made quite great progress in recent years, but the general requirement of C1 [...] Read more.
The High-order Shear Deformation Theories (HSDTs) which can avoid the use of a shear correction factor and better predict the shear behavior of plates have gained extensive recognition and made quite great progress in recent years, but the general requirement of C1 continuity in approximation fields in HSDTs brings difficulties for the numerical implementation of the standard finite element method which is similar to that of the classic Kirchhoff-Love plate theory. As a strong complement to HSDTs, in this work, a series of simple High-order Shear Deformation Triangular Plate Elements (HSDTPEs) using incompatible polynomial approximation are developed for the analysis of isotropic thick-thin plates, cracked plates, and through-thickness functionally graded plates. The elements employ incompatible polynomials to define the element approximation functions u/v/w, and a fictitious thin layer to enforce the displacement continuity among the adjacent plate elements. The HSDTPEs are free from shear-locking, avoid the use of a shear correction factor, and provide stable solutions for thick and thin plates. A variety of numerical examples are solved to demonstrate the convergence, accuracy, and robustness of the present HSDTPEs. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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Review

Jump to: Research

Open AccessReview Continuum Damage-Healing and Super Healing Mechanics in Brittle Materials: A State-of-the-Art Review
Appl. Sci. 2018, 8(12), 2350; https://doi.org/10.3390/app8122350
Received: 21 October 2018 / Revised: 12 November 2018 / Accepted: 13 November 2018 / Published: 22 November 2018
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Abstract
Over the last several years, self-healing materials have become more and more popular in terms of damage reparation. Moreover, a recent theoretical investigation of super healing materials that aims at repairing and strengthening itself was also developed. This research area is well known [...] Read more.
Over the last several years, self-healing materials have become more and more popular in terms of damage reparation. Moreover, a recent theoretical investigation of super healing materials that aims at repairing and strengthening itself was also developed. This research area is well known by the rich experimental studies compared to the numerical investigations. This paper provides a review of the literature of continuum damage-healing and super healing mechanics of brittle materials based on continuum damage and healing mechanics. This review includes various damage-healing models, methodologies, hypotheses and advances in continuum damage and healing mechanics. The anisotropic formulations of damage and healing mechanics are also highlighted. The objective of this paper is also to review the super healing theory based on continuum damage-healing mechanics and its role in material and structure strengthening. Finally, a conclusion of the reviewed damage-healing models is pointed out and future perspectives are given. Full article
(This article belongs to the Special Issue Computational Methods for Fracture)
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