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| List of Figures | |
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| List of Tables | |
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| Preface | |
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| Acknowledgments | |
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| Historical Review and Fundamentals | |
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| Definitions and basic formulations | |
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| Definitions of the J[subscript k] integral vector, M integral, and L integral | |
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| Path selections and conservation laws | |
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| Discussion of previous investigations for invariant integrals | |
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| Physical meanings of the M integral and the L integral | |
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| Nondestructive evaluation of the J and M integrals | |
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| Techniques for experimentally evaluating J and M | |
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| Edge crack | |
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| Evaluation of the M integral | |
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| Center crack | |
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| Brief Summary | |
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| Conservation Laws in Brittle Solids | |
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| Historical reviews and engineering backgrounds | |
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| Independence of the M integral from the origin selection of the global coordinates | |
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| Application of the M integral in multiple crack interacting problems | |
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| Independence of the M integral from the origin selection of the coordinates | |
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| Numerical examples | |
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| Four regularly distributed microcracks | |
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| Randomly distributed microcracks | |
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| Short summary | |
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| Conservation laws in bimaterials | |
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| Conservation laws of the J[subscript k] vector in bimaterials | |
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| Independence of the M integral from the coordinate selection in bimaterials | |
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| M integral analysis for microcrack damage in the brittle phase | |
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| A half-plane brittle solid containing multiple cracks | |
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| Brief summary | |
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| The Projected Conservation Law of J[subscript K] Vector in Microcrack Shielding Problems | |
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| Microcrack shielding problems | |
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| A continuum theory of microcrack shielding | |
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| A discrete modelling of shielding problems | |
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| Fundamental solutions | |
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| Pseudo-traction methods and integral equations | |
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| Numerical examinations | |
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| The J integral analysis: the projected conservation law of the Jk vector | |
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| Numerical results and discussions | |
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| Effect of the T stress | |
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| What is the T stress? | |
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| What role does the T stress play in microcrack shielding problems? | |
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| Brief summary | |
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| Application of the Conservation Laws in Metal/Ceramic Bimaterials | |
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| Fundamental solutions for an interface crack and a sub-interface crack | |
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| Pseudo-traction methods and Fredholm integral equations | |
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| The J integral analysis: the projected conservation law of the J[subscript k] vector | |
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| Numerical examples and discussions | |
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| Brief summary | |
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| Macrocrack Microcrack Interaction in Dissimilar Anisotropic Materials | |
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| Fundamental formulations in dissimilar anisotropic materials | |
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| Fundamental solution for an interface crack | |
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| Fundamental solution for an edge dislocation | |
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| Remote loading conditions | |
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| Superimposing technique and singular integral equations | |
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| Decomposition of the original problem | |
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| Solution of the integral equations | |
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| Analysis of the J integral | |
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| Conservation law of the J integral | |
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| Calculation of the J[subscript 2] integral | |
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| Multiple microcracks situation | |
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| Numerical results and consistency check | |
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| Composite material properties | |
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| Crack interaction configuration and numerical results | |
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| In homogeneous anisotropic cases | |
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| Different dissimilar materials combinations | |
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| The T stress effect | |
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| Brief Summary | |
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| Macrocrack Microcrack Interaction in Piezoelectric Materials | |
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| Elementary solutions | |
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| Elementary solutions for a finite crack | |
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| Elementary solutions for a semi-infinite crack | |
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| Remote loading conditions | |
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| Pseudo-traction electric displacement method (PTED) | |
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| Conservation law and consistency check | |
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| The mechanical strain energy release rate (MSERR) | |
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| Variable tendencies of the SIF owing to microcracking | |
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| Variable tendencies of the EDIF against the location angle | |
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| Variable tendencies of the mechanical strain energy release rate (MSERR) | |
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| Oriented microcrack | |
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| Brief Summary | |
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| Microcrack Damage in Piezoelectric Materials | |
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| General description of the present problem | |
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| J[subscript k] vector in piezoelectric media: physical interpretation and conservation laws | |
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| Path independence of the two components of the J[subscript k] vector | |
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| Conservation laws: statement | |
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| Mathematical proof of conservation laws | |
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| Numerical techniques and examples | |
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| Pseudo-traction electric displacement method | |
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| Numerical results | |
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| Applications: two arbitrarily located interacting cracks | |
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| Brief Summary | |
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| Some other Developments of the Conservation Laws and Energy Release Rates | |
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| Application of the M integral to the Zener crack | |
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| Conservation laws in functional materials | |
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| Energy Momentum Tensor in piezoelectric materials | |
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| Energy momentum tensor in functional materials | |
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| Bueckner's work conjugate integral in piezoelectric materials | |
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| Application of conservation laws of invariant integrals in nanostructures | |
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| Summary | |
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| Index | |