Fracture Analysis

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Soheil Mohammadi - One of the best experts on this subject based on the ideXlab platform.

  • finite strain Fracture Analysis using the extended finite element method with new set of enrichment functions
    International Journal for Numerical Methods in Engineering, 2015
    Co-Authors: Reza Rashetnia, Soheil Mohammadi
    Abstract:

    Summary Nonlinear Fracture Analysis of rubber-like materials is computationally challenging due to a number of complicated numerical problems. The aim of this paper is to study finite strain Fracture problems based on appropriate enrichment functions within the extended finite element method. Two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method. Complex mixed-mode problems under extreme large deformation regimes are solved to evaluate the performance of the proposed extended finite element Analysis based on different tip enrichment functions. Finally, it is demonstrated that the logarithmic set of enrichment functions provides the most accurate and efficient solution for finite strain Fracture Analysis. Copyright © 2015 John Wiley & Sons, Ltd.

  • t spline based xiga for Fracture Analysis of orthotropic media
    Computers & Structures, 2015
    Co-Authors: Sh S Ghorashi, Soheil Mohammadi, N Valizadeh, Timon Rabczuk
    Abstract:

    Fracture Analysis of orthotropic cracked media is investigated by applying the recently developed extended isogeometric Analysis (XIGA) (Ghorashi et al., 2012) using the T-spline basis functions. The signed distance function and orthotropic crack tip enrichment functions are adopted for extrinsically enriching the conventional isogeometric Analysis approximation for representation of strong discontinuity and reproducing the stress singular field around a crack tip, respectively. Moreover, by applying the T-spline basis functions, XIGA is further developed to make the local refinement feasible. For increasing the integration accuracy, the 'sub-triangle' and 'almost polar' techniques are adopted for the cut and crack tip elements, respectively. The interaction integral technique developed by Kim and Paulino (2003) is applied for computing the mixed mode stress intensity factors (SIFs). Finally, the proposed approach is applied for Analysis of some cracked orthotropic problems and the mixed mode SIFs are compared with those of other methods available in the literature.

  • XFEM Fracture Analysis of shells: The effect of crack tip enrichments
    Computational Materials Science, 2011
    Co-Authors: H. Bayesteh, Soheil Mohammadi
    Abstract:

    Abstract In this study the effect of crack tip enrichment functions in the extended finite element Analysis of shells is investigated. Utilization of crack tip enrichments leads to reduction of the required number of elements, mesh independency and increased accuracy in computation of Fracture mechanics parameters such as the stress intensity factor, the crack tip opening displacement and the crack tip opening angle. The procedure is verified by modeling various shell and plate problems and available benchmark tests. Also, effects of enrichments of in-plane, out-of-plane and rotational degrees of freedom and high order out-of-plane enrichments on different Fracture modes are studied. Moreover, reduction of the dependency of crack tip opening angle on the element size in crack propagation problems is discussed.

  • extended finite element method for Fracture Analysis of structures
    2008
    Co-Authors: Soheil Mohammadi
    Abstract:

    Dedication. Preface . Nomenclature . Chapter 1 Introduction. 1.1 Analysis OF STRUCTURES. 1.2 Analysis OF DISCONTINUITIES. 1.3 Fracture MECHANICS. 1.4 CRACK MODELLING. 1.4.1 Local and non-local models. 1.4.2 Smeared crack model. 1.4.3 Discrete inter-element crack. 1.4.4 Discrete cracked element. 1.4.5 Singular elements. 1.4.6 Enriched elements. 1.5 ALTERNATIVE TECHNIQUES. 1.6 A REVIEW OF XFEM APPLICATIONS. 1.6.1 General aspects of XFEM. 1.6.2 Localisation and Fracture. 1.6.3 Composites. 1.6.4 Contact. 1.6.5 Dynamics. 1.6.6 Large deformation/shells. 1.6.7 Multiscale. 1.6.8 Multiphase/solidification. 1.7 SCOPE OF THE BOOK. Chapter 2 Fracture Mechanics, a Review. 2.1 INTRODUCTION. 2.2 BASICS OF ELASTICITY. 2.2.1 Stress-strain relations. 2.2.2 Airy stress function. 2.2.3 Complex stress functions. 2.3 BASICS OF LEFM. 2.3.1 Fracture mechanics. 2.3.2 Circular hole. 2.3.3 Elliptical hole. 2.3.4 Westergaard Analysis of a sharp crack. 2.4 STRESS INTENSITY FACTOR, K . 2.4.1 Definition of the stress intensity factor. 2.4.2 Examples of stress intensity factors for LEFM. 2.4.3 Griffith theories of strength and energy. 2.4.4 Brittle material. 2.4.5 Quasi-brittle material. 2.4.6 Crack stability. 2.4.7 Fixed grip versus fixed load. 2.4.8 Mixed mode crack propagation. 2.5 SOLUTION PROCEDURES FOR K AND G . 2.5.1 Displacement extrapolation/correlation method. 2.5.2 Mode I energy release rate. 2.5.3 Mode I stiffness derivative/virtual crack model. 2.5.4 Two virtual crack extensions for mixed mode cases. 2.5.5 Single virtual crack extension based on displacement decomposition. 2.5.6 Quarter point singular elements. 2.6 ELASTOPLASTIC Fracture MECHANICS (EPFM). 2.6.1 Plastic zone. 2.6.2 Crack tip opening displacements (CTOD). 2.6.3 J integral. 2.6.4 Plastic crack tip fields. 2.6.5 Generalisation of J . 2.7 NUMERICAL METHODS BASED ON THE J INTEGRAL. 2.7.1 Nodal solution. 2.7.2 General finite element solution. 2.7.3 Equivalent domain integral (EDI) method. 2.7.4 Interaction integral method. Chapter 3 Extended Finite Element Method for Isotropic Problems. 3.1 INTRODUCTION. 3.2 A REVIEW OF XFEM DEVELOPMENT. 3.3 BASICS OF FEM. 3.3.1 Isoparametric finite elements, a short review. 3.3.2 Finite element solutions for Fracture mechanics. 3.4 PARTITION OF UNITY. 3.5 ENRICHMENT. 3.5.1 Intrinsic enrichment. 3.5.2 Extrinsic enrichment. 3.5.3 Partition of unity finite element method. 3.5.4 Generalised finite element method. 3.5.5 Extended finite element method. 3.5.6 Hp-clouds enrichment. 3.5.7 Generalisation of the PU enrichment. 3.5.8 Transition from standard to enriched approximation. 3.6 ISOTROPIC XFEM. 3.6.1 Basic XFEM approximation. 3.6.2 Signed distance function. 3.6.3 Modelling strong discontinuous fields. 3.6.4 Modelling weak discontinuous fields. 3.6.5 Plastic enrichment. 3.6.6 Selection of nodes for discontinuity enrichment. 3.6.7 Modelling the crack. 3.7 DISCRETIZATION AND INTEGRATION. 3.7.1 Governing equation. 3.7.2 XFEM discretization. 3.7.3 Element partitioning and numerical integration. 3.7.4 Crack intersection. 3.8 TRACKING MOVING BOUNDARIES. 3.8.1 Level set method. 3.8.2 Fast marching method. 3.8.3 Ordered upwind method. 3.9 NUMERICAL SIMULATIONS. 3.9.1 A tensile plate with a central crack. 3.9.2 Double edge cracks. 3.9.3 Double internal collinear cracks. 3.9.4 A central crack in an infinite plate. 3.9.5 An edge crack in a finite plate. Chapter 4 XFEM for Orthotropic Problems. 4.1 INTRODUCTION. 4.2 ANISOTROPIC ELASTICITY. 4.2.1 Elasticity solution. 4.2.2 Anisotropic stress functions. 4.2.3 Orthotropic mixed mode problems. 4.2.4 Energy release rate and stress intensity factor for anisotropic. materials. 4.2.5 Anisotropic singular elements. 4.3 ANALYTICAL SOLUTIONS FOR NEAR CRACK TIP. 4.3.1 Near crack tip displacement field (class I). 4.3.2 Near crack tip displacement field (class II). 4.3.3 Unified near crack tip displacement field (both classes). 4.4 ANISOTROPIC XFEM. 4.4.1 Governing equation. 4.4.2 XFEM discretization. 4.4.3 SIF calculations. 4.5 NUMERICAL SIMULATIONS. 4.5.1 Plate with a crack parallel to material axis of orthotropy. 4.5.2 Edge crack with several orientations of the axes of orthotropy. 4.5.3 Single edge notched tensile specimen with crack inclination. 4.5.4 Central slanted crack. 4.5.5 An inclined centre crack in a disk subjected to point loads. 4.5.6 A crack between orthotropic and isotropic materials subjected to. tensile tractions. Chapter 5 XFEM for Cohesive Cracks. 5.1 INTRODUCTION. 5.2 COHESIVE CRACKS. 5.2.1 Cohesive crack models. 5.2.2 Numerical models for cohesive cracks. 5.2.3 Crack propagation criteria. 5.2.4 Snap-back behaviour. 5.2.5 Griffith criterion for cohesive crack. 5.2.6 Cohesive crack model. 5.3 XFEM FOR COHESIVE CRACKS. 5.3.1 Enrichment functions. 5.3.2 Governing equations. 5.3.3 XFEM discretization. 5.4 NUMERICAL SIMULATIONS. 5.4.1 Mixed mode bending beam. 5.4.2 Four point bending beam. 5.4.3 Double cantilever beam. Chapter 6 New Frontiers. 6.1 INTRODUCTION. 6.2 INTERFACE CRACKS. 6.2.1 Elasticity solution for isotropic bimaterial interface. 6.2.2 Stability of interface cracks. 6.2.3 XFEM approximation for interface cracks. 6.3 CONTACT. 6.3.1 Numerical models for a contact problem. 6.3.2 XFEM modelling of a contact problem. 6.4 DYNAMIC Fracture. 6.4.1 Dynamic crack propagation by XFEM. 6.4.2 Dynamic LEFM. 6.4.3 Dynamic orthotropic LEFM. 6.4.4 Basic formulation of dynamic XFEM. 6.4.5 XFEM discretization. 6.4.6 Time integration. 6.4.7 Time finite element method. 6.4.8 Time extended finite element method. 6.5 MULTISCALE XFEM. 6.5.1 Basic formulation. 6.5.2 The zoom technique. 6.5.3 Homogenisation based techniques. 6.5.4 XFEM discretization. 6.6 MULTIPHASE XFEM. 6.6.1 Basic formulation. 6.6.2 XFEM approximation. 6.6.3 Two-phase fluid flow. 6.6.4 XFEM approximation. Chapter 7 XFEM Flow. 7.1 INTRODUCTION. 7.2 AVAILABLE OPEN-SOURCE XFEM. 7.3. FINITE ELEMENT Analysis. 7.3.1 Defining the model. 7.3.2 Creating the finite element mesh. 7.3.3 Linear elastic Analysis. 7.3.4 Large deformation. 7.3.5 Nonlinear (elastoplastic) Analysis. 7.3.6 Material constitutive matrix. 7.4 XFEM. 7.4.1 Front tracking. 7.4.2 Enrichment detection. 7.4.3 Enrichment functions. 7.4.4 Ramp (transition) functions. 7.4.5 Evaluation of the B matrix. 7.5 NUMERICAL INTEGRATION. 7.5.1 Sub-quads. 7.5.2 Sub-triangles. 7.6 SOLVER. 7.6.1 XFEM degrees of freedom. 7.6.2 Time integration. 7.6.3 Simultaneous equations solver. 7.6.4 Crack length control. 7.7 POST-PROCESSING. 7.7.1 Stress intensity factor. 7.7.2 Crack growth. 7.7.3 Other applications. 7.8 CONFIGURATION UPDATE. References . Index

Yourui Tao - One of the best experts on this subject based on the ideXlab platform.

  • stable node based smoothed extended finite element method for Fracture Analysis of structures
    Computers & Structures, 2020
    Co-Authors: J W Zhao, S Z Feng, Yourui Tao
    Abstract:

    Abstract Based on low-order elements, a stable node-based smoothed extended finite element method (SNS-XFEM) is proposed for Fracture Analysis of structures in this study. For the proposed method, the problem domain is discretized using low-order elements, which can be easily generated for structures with complex shapes. The node-based smoothing domains are then generated to perform the strain smoothing technique, which can effectively avoid singular integration. The discontinuity caused by crack is modeled using enrichment functions and a stabilization term based on strain gradient is also taken into account to further improve the accuracy. Finally, some numerical cases are studied to fully investigate the performance of present method. The obtained results show that the proposed SNS-XFEM can perform much better than standard XFEM and NS-XFEM.

Yongdong Li - One of the best experts on this subject based on the ideXlab platform.

  • anti plane Fracture Analysis for the weak discontinuous interface in a non homogeneous piezoelectric bi material structure
    European Journal of Mechanics A-solids, 2009
    Co-Authors: Yongdong Li
    Abstract:

    The concept of weak discontinuity is extended to functionally graded piezoelectric bi-material interface, and Fracture Analysis for the weak discontinuous interface is performed by the methods of Fourier integral transform and Cauchy singular integral equation. Numerical results of the total energy release rate (TERR) and the mechanical strain energy release rate (MSERR) are obtained to show the effects of non-homogeneity parameters, geometrical parameters and loads. Parametric studies yield three conclusions: (1) To reduce the weak-discontinuity of the interface is beneficial to resisting interfacial Fracture. The effect of the weak-discontinuity of the interface on TERR and MSERR still depends on the strip width. The wider the strip, the more sensitive the TERR and MSERR will be to the weak-discontinuity of the interface. (2) To predict the effect of electric load on crack propagation, MSERR is more appropriate than TERR to be used as a Fracture parameter. To predict the effect of mechanical load on crack propagation, both of them could be used as Fracture parameters, and MSERR is more conservative. (3) Mechanical load and negative electric displacement load would promote crack propagation, but positive electric displacement load would retard it. For the structure applied by combined mechanical and positive electric displacement loads, crack propagation may be impeded by appropriately selecting the strip width and the ratio of non-homogeneity parameters.

  • Fracture Analysis of a weak discontinuous interface in a symmetrical functionally gradient composite strip loaded by anti plane impact
    Archive of Applied Mechanics, 2008
    Co-Authors: Yongdong Li
    Abstract:

    The anti-plane impact Fracture Analysis was performed for a weak-discontinuous interface in a symmetrical functionally gradient composite strip. A new bi-parameter exponential function was introduced to simulate the continuous variation of material properties. Using Laplace and Fourier integral transforms, we reduced the problem to a dual integral equation and obtained asymptotic analytical solution of crack-tip stress field. Based on the numerical solution of the second kind of Fredholm integral equation transformed from the dual integral equation, the effects of the two non-homogeneity parameters on DSIF were discussed. It was indicated that the relative stiffness of the interface and the general stiffness of the whole structure are two important factors affecting the impact Fracture behavior of the weak-discontinuous interface. The greater the relative stiffness of the interface is, the higher the value of the dynamic stress intensity factor will be. The greater the general stiffness of the whole structure is, the shorter the time for DSIF to arrive at the peak value and then to stabilize to the steady one. If the general stiffness of the whole structure is great enough, there will be an oscillation between the peak and steady values of DSIF.

  • Fracture Analysis of functionally gradient weak micro discontinuous interface with finite element method
    Computational Materials Science, 2006
    Co-Authors: Yongdong Li, Hongcai Zhang
    Abstract:

    Abstract The main idea of this paper is to study the influence of the discontinuity of mechanical property of FGMs on the stress intensity factors by means of FEM calculations. The FGMs interface is classified into four kinds according to the discontinuity of mechanical properties and their derivatives across it. Mechanical models were established for Fracture Analysis of the functionally gradient elastic weak/micro-discontinuous interfaces. Finite element method was used to obtain SIFs of the interfacial crack, based on the discussion of which three methods to diminish SIFs were suggested: (a) to increase the sizes of the FGMs plates; (b) to reduce the weak-discontinuity of FGMs interface; (c) to make FGMs interface micro-discontinuous. A simple method to make FGMs interface micro-discontinuous is to make mechanical property of the FGM at one side of the interface to be the lower-rank polynomial truncated from Taylor series of that of the FGM at the other side. The first-rank micro-discontinuity is always enough to reduce SIFs notably, so, it is not necessary to manufacture FGMs interface with higher-rank micro-discontinuity in engineering.

J W Zhao - One of the best experts on this subject based on the ideXlab platform.

  • stable node based smoothed extended finite element method for Fracture Analysis of structures
    Computers & Structures, 2020
    Co-Authors: J W Zhao, S Z Feng, Yourui Tao
    Abstract:

    Abstract Based on low-order elements, a stable node-based smoothed extended finite element method (SNS-XFEM) is proposed for Fracture Analysis of structures in this study. For the proposed method, the problem domain is discretized using low-order elements, which can be easily generated for structures with complex shapes. The node-based smoothing domains are then generated to perform the strain smoothing technique, which can effectively avoid singular integration. The discontinuity caused by crack is modeled using enrichment functions and a stabilization term based on strain gradient is also taken into account to further improve the accuracy. Finally, some numerical cases are studied to fully investigate the performance of present method. The obtained results show that the proposed SNS-XFEM can perform much better than standard XFEM and NS-XFEM.

S Z Feng - One of the best experts on this subject based on the ideXlab platform.

  • stable node based smoothed extended finite element method for Fracture Analysis of structures
    Computers & Structures, 2020
    Co-Authors: J W Zhao, S Z Feng, Yourui Tao
    Abstract:

    Abstract Based on low-order elements, a stable node-based smoothed extended finite element method (SNS-XFEM) is proposed for Fracture Analysis of structures in this study. For the proposed method, the problem domain is discretized using low-order elements, which can be easily generated for structures with complex shapes. The node-based smoothing domains are then generated to perform the strain smoothing technique, which can effectively avoid singular integration. The discontinuity caused by crack is modeled using enrichment functions and a stabilization term based on strain gradient is also taken into account to further improve the accuracy. Finally, some numerical cases are studied to fully investigate the performance of present method. The obtained results show that the proposed SNS-XFEM can perform much better than standard XFEM and NS-XFEM.

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