Applications of the Variational Approach to Fracture Mechanics PDF Download
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Author: Ataollah Mesgarnejad
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Ataollah Mesgarnejad
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Blaise Bourdin
Publisher: Springer Science & Business Media
ISBN: 1402063954
Category : Technology & Engineering
Languages : en
Pages : 173
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Book Description
Presenting original results from both theoretical and numerical viewpoints, this text offers a detailed discussion of the variational approach to brittle fracture. This approach views crack growth as the result of a competition between bulk and surface energy, treating crack evolution from its initiation all the way to the failure of a sample. The authors model crack initiation, crack path, and crack extension for arbitrary geometries and loads.
Author: Ataollah Mesgarnejad
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Gianpietro Del Piero
Publisher: Springer Science & Business Media
ISBN: 9400772262
Category : Science
Languages : en
Pages : 89
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Book Description
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 In the year and a half elapsed after the course, the material has been revised and enriched with new and partially unpublished results.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. Reprinted from the Journal of Elasticity, volume 112, issue 1, 2013.
Author: Roberto Alessi
Publisher:
ISBN:
Category :
Languages : en
Pages : 204
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Author: Francesco dell'Isola
Publisher: Springer Science & Business Media
ISBN: 3709109833
Category : Technology & Engineering
Languages : en
Pages : 363
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Book Description
F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
Author: Ted L. Anderson
Publisher: CRC Press
ISBN: 1420058215
Category : Science
Languages : en
Pages : 630
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Book Description
With its combination of practicality, readability, and rigor that is characteristic of any truly authoritative reference and text, Fracture Mechanics: Fundamentals and Applications quickly established itself as the most comprehensive guide to fracture mechanics available. It has been adopted by more than 100 universities and embraced by thousands of professional engineers worldwide. Now in its third edition, the book continues to raise the bar in both scope and coverage. It encompasses theory and applications, linear and nonlinear fracture mechanics, solid mechanics, and materials science with a unified, balanced, and in-depth approach. Reflecting the many advances made in the decade since the previous edition came about, this indispensable Third Edition now includes: A new chapter on environmental cracking Expanded coverage of weight functions New material on toughness test methods New problems at the end of the book New material on the failure assessment diagram (FAD) method Expanded and updated coverage of crack closure and variable-amplitude fatigue Updated solutions manual In addition to these enhancements, Fracture Mechanics: Fundamentals and Applications, Third Edition also includes detailed mathematical derivations in appendices at the end of applicable chapters; recent developments in laboratory testing, application to structures, and computational methods; coverage of micromechanisms of fracture; and more than 400 illustrations. This reference continues to be a necessity on the desk of anyone involved with fracture mechanics.
Author: E.E. Gdoutos
Publisher: Springer Science & Business Media
ISBN: 9400919565
Category : Science
Languages : en
Pages : 326
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Book Description
It is difficult to do justice to fracture mechanics in a textbook, for the subject encompasses so many disciplines. A general survey of the field would serve no purpose other than give a collection of references. The present book by Professor E. E. Gdoutos is refreshing because it does not fall into the esoteric tradition of outlining equations and results. Basic ideas and underlying principles are clearly explained as to how they are used in application. The presentations are concise and each topic can be understood by advanced undergraduates in material science and continuum mechanics. The book is highly recommended not only as a text in fracture mechanics but also as a reference to those interested in the general aspects of failure analysis. In addition to providing an in-depth review of the analytical methods for evaluating the fundamental quantities used in linear elastic fracture mechanics, various criteria are discussed re:O. ecting their limitations and applications. Par ticular emphases are given to predicting crack initiation, subcritical growth and the onset of rapid fracture from a single criterion. Those models in which it is assumed that the crack extends from tip to tip rely on the specific surface energy concept. The differences in the global and energy states before and after crack extension were associated with the energy required to create a unit area of crack surface. Applications were limited by the requirement of self-similar crack growth.
Author: Bin Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 113
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Book Description
Fracture mechanics of brittle materials has focused on bulk materials with isotropic surface energy. In this situation different physical principles for crack path selection are very similar or even equivalent. The situation is radically different when considering crack propagation in brittle materials with anisotropic surface energy. Such materials are important in applications involving single crystals, extruded polymers, or geological and organic materials. When this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. Thus, this situation interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Similarly, tearing of brittle thin elastic sheets, ubiquitous in nature, technology and daily life, challenges our understanding of fracture. Since tearing typically involves large geometric nonlinearity, it is not clear whether the stress intensity factors are meaningful or if and how they determine crack propagation. Geometry, together with the interplay between stretching and bending deformation, leads to complex behaviors, restricting analytical approximate solutions to very simplified settings and specific parameter regimes. In both situations, a rich and nontrivial experimental record has been successfully understood in terms of simple energetic models. However, general modeling approaches to either fracture in the presence of strong surface energy anisotropy or to tearing, capable of exploring new physics, have been lacking. The success of energetic simple models suggests that variational theories of brittle fracture may provide a unifying and general framework capable of dealing with the more general situations considered here. To address fracture in materials with strongly anisotropic surface energy, we propose a variational phase-field model resorting to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture, and reproduce strikingly well recent experimental observations. To explore tearing of thin films, we develop a geometrically exact model and a computational framework coupling elasticity (stretching and bending), fracture, and adhesion to a substrate. We numerically implement the model with subdivision surface finite elements. Our simulations qualitatively and quantitatively reproduced the crack patterns observed in tearing experiments. Finally, we examine how shell geometry affects fracture. As suggested by previous results and our own phase-field simulations, shell shape dramatically affects crack evolution and the effective toughness of the shell structure. To gain insight and eventually develop new concepts for optimizing the design of thin shell structures, we derive the configurational force conjugate to crack extension for Koiter's linear thin shell theory. We identify the conservative contribution to this force through an Eshelby tensor, as well as non-conservative contributions arising from curvature.
Author: S. Nemat-Nasser
Publisher: Elsevier
ISBN: 1483145832
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
Variational Methods in the Mechanics of Solids contains the proceedings of the International Union of Theoretical and Applied Mechanics Symposium on Variational Methods in the Mechanics of Solids, held at Northwestern University in Evanston, Illinois, on September 11-13, 1978. The papers focus on advances in the application of variational methods to a variety of mathematically and technically significant problems in solid mechanics. The discussions are organized around three themes: thermomechanical behavior of composites, elastic and inelastic boundary value problems, and elastic and inelastic dynamic problems. This book is comprised of 58 chapters and opens by addressing some questions of asymptotic expansions connected with composite and with perforated materials. The following chapters explore mathematical and computational methods in plasticity; variational irreversible thermodynamics of open physical-chemical continua; macroscopic behavior of elastic material with periodically spaced rigid inclusions; and application of the Lanczos method to structural vibration. Finite deformation of elastic beams and complementary theorems of solid mechanics are also considered, along with numerical contact elastostatics; periodic solutions in plasticity and viscoplasticity; and the convergence of the mixed finite element method in linear elasticity. This monograph will appeal to practitioners of mathematicians as well as theoretical and applied mechanics.
