| Description |
1 online resource (100 pages) : color illustrations |
| Contents |
Lecture 1. Brittle Fracture -- Two Elementary Problems in the Calculus of Variations -- A Model for Brittle Fracture -- Equilibrium Configurations -- Stability -- Quasi-Static Evolutions -- Crack Initiation -- Comments -- Historical Note -- Lecture 2. Regularization Cohesive Energies -- Equilibrium Configurations -- Stability -- Equilibrium Curves -- Response Curves -- Energy Landscapes -- References and Comments -- Lecture 3. Microstructures -- Convex-Concave Energies -- Generalized Configurations -- Equilibrium Microstructures -- Stable Microstructures -- Response Curves -- A Glance at Other Cohesive Energies -- References and Comments -- Lecture 4. Irreversibility -- Dissipative Character of the Cohesive Energy -- Pre-Fractured Equilibrium Configurations -- Stability -- Quasi-Static Evolutions -- References and Comments -- Lecture 5. Diffuse Fracture: The Local Model -- Bulk Cohesive Energies -- Equilibrium -- Stability -- Quasi-Static Evolutions -- References and Comments -- Lecture 6. Diffuse Fracture: The Non-local Model -- Basic Assumptions -- Equilibrium -- Stability -- Quasi-Static Evolutions -- The Onset of the Inelastic Regime -- Internal Lengths -- Numerical Simulations -- References and Comments -- Closure |
| Summary |
This book exposes a number of mathematical models for fracture of growing difficulty. All models are treated in a unified way, based on incremental energy minimization. They differ from each other by the assumptions made on the inelastic part of the total energy, here called the "cohesive energy". Each model describes a specific aspect of material response, and particular care is devoted to underline the correspondence of each model to the experiments. The content of the book is a re-elaboration of the lectures delivered at the First Sperlonga Summer School on Mechanics and Engineering Sciences in September 2011. In the year and a half elapsed after the course, the material has been revised and enriched with new and partially unpublished results. Significant additions have been introduced in the occasion of the course "The variational approach to fracture and other inelastic phenomena", delivered at SISSA, Trieste, in March 2013. The Notes reflect a research line carried on by the writer over the years, addressed to a comprehensive description of the many aspects of the phenomenon of fracture, and to its relations with other phenomena, such as the formation of microstructure and the changes in the material's strength induced by plasticity and damage |
| Notes |
"Previously published in Journal of elasticity, volume 112, issue 1, 2013." |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed September 3, 2013) |
| Subject |
Fracture mechanics -- Mathematical models
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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TECHNOLOGY & ENGINEERING -- Reference.
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Ingénierie.
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Fracture mechanics -- Mathematical models
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| Form |
Electronic book
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| ISBN |
9789400772267 |
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9400772262 |
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