XFEM Fracture Analysis of Composites

Inbunden, Engelska, 2012

Av Soheil Mohammadi, University of Tehran) Mohammadi, Soheil (School of Civil Engineering

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This book describes the basics and developments of the new XFEM approach to fracture analysis of composite structures and materials. It provides state of the art techniques and algorithms for fracture analysis of structures including numeric examples at the end of each chapter as well as an accompanying website which will include MATLAB resources, executables, data files, and simulation procedures of XFEM. The first reference text for the extended finite element method (XFEM) for fracture analysis of structures and materialsIncludes theory and applications, with worked numerical problems and solutions, and MATLAB examples on an accompanying website with further XFEM resourcesProvides a comprehensive overview of this new area of research, including a review of Fracture Mechanics, basic through to advanced XFEM theory, as well as current problems and applicationsIncludes a chapter on the future developments in the field, new research areas and possible future applications of the method

Produktinformation

Utgivningsdatum2012-09-21
Mått173 x 253 x 23 mm
Vikt739 g
FormatInbunden
SpråkEngelska
Antal sidor400
FörlagJohn Wiley & Sons Inc
ISBN9781119974062

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Soheil Mohammadi, Associate Professor, School of Civil Engineering, University of Tehran, Tehran, IRANSoheil Mohammdi studied for his PhD at the University of Wales Swansea and is now a lecturer at the University of Tehran where his academic career began. He teaches PhD courses in contact mechanics, mesh generation and adaptivity, meshless methods, and impact and explosive loadings on structures. He research interests are based in computational mechanics and finite element analysis, and XFEM. He has published many papers in these areas as well as a book on discontinuum mechanics in 2003.

Preface xiiiNomenclature xvii1 Introduction 11.1 Composite Structures 11.2 Failures of Composites 21.2.1 Matrix Cracking 21.2.2 Delamination 21.2.3 Fibre/Matrix Debonding 21.2.4 Fibre Breakage 31.2.5 Macro Models of Cracking in Composites 31.3 Crack Analysis 31.3.1 Local and Non-Local Formulations 31.3.2 Theoretical Methods for Failure Analysis 51.4 Analytical Solutions for Composites 61.4.1 Continuum Models 61.4.2 Fracture Mechanics of Composites 61.5 Numerical Techniques 81.5.1 Boundary Element Method 81.5.2 Finite Element Method 81.5.3 Adaptive Finite/Discrete Element Method 101.5.4 Meshless Methods 101.5.5 Extended Finite Element Method 111.5.6 Extended Isogeometric Analysis 121.5.7 Multiscale Analysis 131.6 Scope of the Book 132 Fracture Mechanics, A Review 172.1 Introduction 172.2 Basics of Elasticity 202.2.1 Stress–Strain Relations 202.2.2 Airy Stress Function 222.2.3 Complex Stress Functions 222.3 Basics of LEFM 232.3.1 Fracture Mechanics 232.3.2 Infinite Tensile Plate with a Circular Hole 242.3.3 Infinite Tensile Plate with an Elliptical Hole 262.3.4 Westergaard Analysis of a Line Crack 282.3.5 Williams Solution of a Wedge Corner 292.4 Stress Intensity Factor, K 302.4.1 Definition of the Stress Intensity Factor 302.4.2 Examples of Stress Intensity Factors for LEFM 332.4.3 Griffith Energy Theories 352.4.4 Mixed Mode Crack Propagation 382.5 Classical Solution Procedures for K and G 412.5.1 Displacement Extrapolation/Correlation Method 412.5.2 Mode I Energy Release Rate 412.5.3 Mode I Stiffness Derivative/Virtual Crack Model 422.5.4 Two Virtual Crack Extensions for Mixed Mode Cases 422.5.5 Single Virtual Crack Extension Based on Displacement Decomposition 432.6 Quarter Point Singular Elements 442.7 J Integral 472.7.1 Generalization of J 482.7.2 Effect of Crack Surface Traction 482.7.3 Effect of Body Force 492.7.4 Equivalent Domain Integral (EDI) Method 492.7.5 Interaction Integral Method 492.8 Elastoplastic Fracture Mechanics (EPFM) 512.8.1 Plastic Zone 512.8.2 Crack-Tip Opening Displacements (CTOD) 532.8.3 J Integral for EPFM 553 Extended Finite Element Method 573.1 Introduction 573.2 Historic Development of XFEM 583.2.1 A Review of XFEM Development 583.2.2 A Review of XFEM Composite Analysis 623.3 Enriched Approximations 623.3.1 Partition of Unity 623.3.2 Intrinsic and Extrinsic Enrichments 633.3.3 Partition of Unity Finite Element Method 663.3.4 MLS Enrichment 663.3.5 Generalized Finite Element Method 673.3.6 Extended Finite Element Method 673.3.7 Generalized PU Enrichment 673.4 XFEM Formulation 673.4.1 Basic XFEM Approximation 683.4.2 Signed Distance Function 693.4.3 Modelling the Crack 703.4.4 Governing Equation 713.4.5 XFEM Discretization 723.4.6 Evaluation of Derivatives of Enrichment Functions 733.4.7 Selection of Nodes for Discontinuity Enrichment 753.4.8 Numerical Integration 773.5 XFEM Strong Discontinuity Enrichments 793.5.1 A Modified FE Shape Function 793.5.2 The Heaviside Function 813.5.3 The Sign Function 843.5.4 Strong Tangential Discontinuity 853.5.5 Crack Intersection 853.6 XFEM Weak Discontinuity Enrichments 863.7 XFEM Crack-Tip Enrichments 873.7.1 Isotropic Enrichment 873.7.2 Orthotropic Enrichment Functions 883.7.3 Bimaterial Enrichments 883.7.4 Orthotropic Bimaterial Enrichments 893.7.5 Dynamic Enrichment 893.7.6 Orthotropic Dynamic Enrichments for Moving Cracks 903.7.7 Bending Plates 913.7.8 Crack-Tip Enrichments in Shells 913.7.9 Electro-Mechanical Enrichment 923.7.10 Dislocation Enrichment 933.7.11 Hydraulic Fracture Enrichment 943.7.12 Plastic Enrichment 943.7.13 Viscoelastic Enrichment 953.7.14 Contact Corner Enrichment 963.7.15 Modification for Large Deformation Problems 973.7.16 Automatic Enrichment 993.8 Transition from Standard to Enriched Approximation 993.8.1 Linear Blending 1003.8.2 Hierarchical Transition Domain 1003.9 Tracking Moving Boundaries 1033.9.1 Level Set Method 1033.9.2 Alternative Methods 1063.10 Numerical Simulations 1073.10.1 A Central Crack in an Infinite Tensile Plate 1073.10.2 An Edge Crack in a Finite Plate 1093.10.3 Tensile Plate with a Central Inclined Crack 1103.10.4 A Bending Plate in Fracture Mode III 1113.10.5 Crack Propagation in a Shell 1123.10.6 Shear Band Simulation 1153.10.7 Fault Simulation 1163.10.8 Sliding Contact Stress Singularity by PUFEM 1193.10.9 Hydraulic Fracture 1223.10.10 Dislocation Dynamics 1264 Static Fracture Analysis of Composites 1314.1 Introduction 1314.2 Anisotropic Elasticity 1344.2.1 Elasticity Solution 1344.2.2 Anisotropic Stress Functions 1364.3 Analytical Solutions for Near Crack Tip 1374.3.1 The General Solution 1374.3.2 Special Solutions for Different Types of Composites 1404.4 Orthotropic Mixed Mode Fracture 1424.4.1 Energy Release Rate for Anisotropic Materials 1424.4.2 Anisotropic Singular Elements 1424.4.3 SIF Calculation by Interaction Integral 1434.4.4 Orthotropic Crack Propagation Criteria 1474.5 Anisotropic XFEM 1494.5.1 Governing Equation 1494.5.2 XFEM Discretization 1504.5.3 Orthotropic Enrichment Functions 1514.6 Numerical Simulations 1524.6.1 Plate with a Crack Parallel to the Material Axis of Orthotropy 1524.6.2 Edge Crack with Several Orientations of the Axes of Orthotropy 1554.6.3 Inclined Edge Notched Tensile Specimen 1564.6.4 Central Slanted Crack 1604.6.5 An Inclined Centre Crack in a Disk Subjected to Point Loads 1644.6.6 Crack Propagation in an Orthotropic Beam 1665 Dynamic Fracture Analysis of Composites 1695.1 Introduction 1695.1.1 Dynamic Fracture Mechanics 1695.1.2 Dynamic Fracture Mechanics of Composites 1705.1.3 Dynamic Fracture by XFEM 1725.2 Analytical Solutions for Near Crack Tips in Dynamic States 1735.2.1 Analytical Solution for a Propagating Crack in Isotropic Material 1745.2.2 Asymptotic Solution for a Stationary Crack in Orthotropic Media 1755.2.3 Analytical Solution for Near Crack Tip of a Propagating Crack in Orthotropic Material 1765.3 Dynamic Stress Intensity Factors 1785.3.1 Stationary and Moving Crack Dynamic Stress Intensity Factors 1785.3.2 Dynamic Fracture Criteria 1795.3.3 J Integral for Dynamic Problems 1805.3.4 Domain Integral for Orthotropic Media 1815.3.5 Interaction Integral 1825.3.6 Crack-Axis Component of the Dynamic J Integral 1835.3.7 Field Decomposition Technique 1855.4 Dynamic XFEM 1855.4.1 Dynamic Equations of Motion 1855.4.2 XFEM Discretization 1855.4.3 XFEM Enrichment Functions 1875.4.4 Time Integration Schemes 1915.5 Numerical Simulations 1955.5.1 Plate with a Stationary Central Crack 1955.5.2 Mode I Plate with an Edge Crack 1965.5.3 Mixed Mode Edge Crack in Composite Plates 1995.5.4 A Composite Plate with Double Edge Cracks under Impulsive Loading 2105.5.5 Pre-Cracked Three Point Bending Beam under Impact Loading 2135.5.6 Propagating Central Inclined Crack in a Circular Orthotropic Plate 2176 Fracture Analysis of Functionally Graded Materials (FGMs) 2256.1 Introduction 2256.2 Analytical Solution for Near a Crack Tip 2276.2.1 Average Material Properties 2276.2.2 Mode I Near Tip Fields in FGM Composites 2286.2.3 Stress and Displacement Field (Similar to Homogeneous Orthotropic Composites) 2336.3 Stress Intensity Factor 2356.3.1 J Integral 2356.3.2 Interaction Integral 2366.3.3 FGM Auxillary Fields 2366.3.4 Isoparametric FGM 2406.4 Crack Propagation in FGM Composites 2406.5 Inhomogeneous XFEM 2416.5.1 Governing Equation 2416.5.2 XFEM Approximation 2416.5.3 XFEM Discretization 2436.6 Numerical Examples 2446.6.1 Plate with a Centre Crack Parallel to the Material Gradient 2446.6.2 Proportional FGM Plate with an Inclined Central Crack 2476.6.3 Non-Proportional FGM Plate with a Fixed Inclined Central Crack 2506.6.4 Rectangular Plate with an Inclined Crack (Non-Proportional Distribution) 2516.6.5 Crack Propagation in a Four-Point FGM Beam 2537 Delamination/Interlaminar Crack Analysis 2617.1 Introduction 2617.2 Fracture Mechanics for Bimaterial Interface Cracks 2647.2.1 Isotropic Bimaterial Interfaces 2657.2.2 Orthotropic Bimaterial Interface Cracks 2667.2.3 Stress Contours for a Crack between Two Dissimilar Orthotropic Materials 2707.3 Stress Intensity Factors for Interlaminar Cracks 2717.4 Delamination Propagation 2737.4.1 Fracture Energy-Based Criteria 2737.4.2 Stress-Based Criteria 2737.4.3 Contact-Based Criteria 2747.5 Bimaterial XFEM 2757.5.1 Governing Equation 2757.5.2 XFEM Discretization 2767.5.3 XFEM Enrichment Functions for Bimaterial Problems 2787.5.4 Discretization and Integration 2807.6 Numerical Examples 2807.6.1 Central Crack in an Infinite Bimaterial Plate 2807.6.2 Isotropic-Orthotropic Bimaterial Crack 2897.6.3 Orthotropic Double Cantilever Beam 2917.6.4 Concrete Beams Strengthened with Fully Bonded GFRP 2947.6.5 FRP Reinforced Concrete Cantilever Beam Subjected to Edge Loadings 2957.6.6 Delamination of Metallic I Beams Strengthened by FRP Strips 2987.6.7 Variable Section Beam Reinforced by FRP 3008 New Orthotropic Frontiers 3038.1 Introduction 3038.2 Orthotropic XIGA 3038.2.1 NURBS Basis Function 3048.2.2 Extended Isogeometric Analysis 3058.2.3 XIGA Simulations 3138.3 Orthotropic Dislocation Dynamics 3218.3.1 Straight Dislocations in Anisotropic Materials 3218.3.2 Edge Dislocations in Anisotropic Materials 3228.3.3 Curve Dislocations in Anisotropic Materials 3248.3.4 Anisotropic Dislocation XFEM 3248.3.5 Plane Strain Anisotropic Solution 3298.3.6 Individual Sliding Systems s1 and s2 in an Infinite Domain 3308.3.7 Simultaneous Sliding Systems in an Infinite Domain 3308.4 Other Anisotropic Applications 3338.4.1 Biomechanics 3338.4.2 Piezoelectric 335References 339Index 363