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The Variational Approach to Fracture

The Variational Approach to Fracture Author Blaise Bourdin
ISBN-10 9781402063954
Release 2008-04-19
Pages 164
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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.



A Variational Approach to Fracture and Other Inelastic Phenomena

A Variational Approach to Fracture and Other Inelastic Phenomena Author Gianpietro Del Piero
ISBN-10 9789400772267
Release 2013-08-30
Pages 80
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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 In the year and a half elapsed after the course, the material has been revised and enriched with new and partially unpublished results.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.



Variational Methods in the Mechanics of Solids

Variational Methods in the Mechanics of Solids Author S. Nemat-Nasser
ISBN-10 9781483145839
Release 2017-01-31
Pages 428
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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.



Variational Analysis and Aerospace Engineering

Variational Analysis and Aerospace Engineering Author Giuseppe Buttazzo
ISBN-10 9780387958576
Release 2009-08-21
Pages 518
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Variational Analysis and Aerospace Engineering has been writing in one form or another for most of life. You can find so many inspiration from Variational Analysis and Aerospace Engineering also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Variational Analysis and Aerospace Engineering book for free.



Numerical and Computer Methods in Structural Mechanics

Numerical and Computer Methods in Structural Mechanics Author Steven J. Fenves
ISBN-10 9781483272542
Release 2014-05-10
Pages 698
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Numerical and Computer Methods in Structural Mechanics is a compendium of papers that deals with the numerical methods in structural mechanics, computer techniques, and computer capabilities. Some papers discus the analytical basis of the computer technique most widely used in software, that is, the finite element method. This method includes the convergence (in terms of variation principles) isoparametrics, hybrid models, and incompatible displacement models. Other papers explain the storage or retrieval of data, as well as equation-solving algorithms. Other papers describe general-purpose structural mechanics programs, alternatives to, and extension of the usual finite element approaches. Another paper explores nonlinear, dynamic finite element problems, and a direct physical approach to determine finite difference models. Special papers explain structural mechanics used in computing, particularly, those related to integrated data bases, such as in the Structures Oriented Exchange System of the Office of Naval Research and the integrated design of tanker structures. Other papers describe software and hardware capabilities, for example, in ship design, fracture mechanics, biomechanics, and crash safety. The text is suitable for programmers, computer engineers, researchers, and scientists involved in materials and industrial design.



Micromechanics of Fracture and Damage

Micromechanics of Fracture and Damage Author Luc Dormieux
ISBN-10 9781119292180
Release 2016-03-31
Pages 332
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This book deals with the mechanics and physics of fractures at various scales. Based on advanced continuum mechanics of heterogeneous media, it develops a rigorous mathematical framework for single macrocrack problems as well as for the effective properties of microcracked materials. In both cases, two geometrical models of cracks are examined and discussed: the idealized representation of the crack as two parallel faces (the Griffith crack model), and the representation of a crack as a flat elliptic or ellipsoidal cavity (the Eshelby inhomogeneity problem). The book is composed of two parts: - The first part deals with solutions to 2D and 3D problems involving a single crack in linear elasticity. Elementary solutions of cracks problems in the different modes are fully worked. Various mathematical techniques are presented, including Neuber-Papkovitch displacement potentials, complex analysis with conformal mapping and Eshelby-based solutions. - The second part is devoted to continuum micromechanics approaches of microcracked materials in relation to methods and results presented in the first part. Various estimates and bounds of the effective elastic properties are presented. They are considered for the formulation and application of continuum micromechanics-based damage models.



Variational Analysis and Aerospace Engineering

Variational Analysis and Aerospace Engineering Author Aldo Frediani
ISBN-10 9783319456805
Release 2017-01-28
Pages 524
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This book presents papers surrounding the extensive discussions that took place from the ‘Variational Analysis and Aerospace Engineering’ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.



Fracture Phenomena in Nature and Technology

Fracture Phenomena in Nature and Technology Author Davide Bigoni
ISBN-10 9783319043975
Release 2014-04-29
Pages 266
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This book contains contributions presented at the IUTAM Symposium "Fracture Phenomena in Nature and Technology" held in Brescia, Italy, 1-5 July, 2012.The objective of the Symposium was fracture research, interpreted broadly to include new engineering and structural mechanics treatments of damage development and crack growth and also large-scale failure processes as exemplified by earthquake or landslide failures, ice shelf break-up and hydraulic fracturing (natural or for resource extraction or CO2 sequestration), as well as small-scale rupture phenomena in materials physics including, e.g. inception of shear banding, void growth, adhesion and decohesion in contact and friction, crystal dislocation processes and atomic/electronic scale treatment of brittle crack tips and fundamental cohesive properties. Special emphasis was given to multiscale fracture description and new scale-bridging formulations capable to substantiate recent experiments and tailored to become the basis for innovative computational algorithms.



Advances in Computational Plasticity

Advances in Computational Plasticity Author Eugenio Oñate
ISBN-10 9783319608853
Release 2017-09-09
Pages 434
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This book brings together some 20 chapters on state-of-the-art research in the broad field of computational plasticity with applications in civil and mechanical engineering, metal forming processes, geomechanics, nonlinear structural analysis, composites, biomechanics and multi-scale analysis of materials, among others. The chapters are written by world leaders in the different fields of computational plasticity.



Hybrid and Incompatible Finite Element Methods

Hybrid and Incompatible Finite Element Methods Author Theodore H.H. Pian
ISBN-10 9781135442217
Release 2005-11-04
Pages 400
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While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances--many directly attributable to these authors--have allowed the development of the stability theory and abstract mathematics to useful tools. Hybrid and Incompatible Finite Element Methods introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.



Models and Phenomena in Fracture Mechanics

Models and Phenomena in Fracture Mechanics Author Leonid I. Slepyan
ISBN-10 9783540480105
Release 2012-11-07
Pages 576
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Presenting the most important results, methods, and open questions, this book describes and compares advanced models in fracture mechanics. The author introduces the required mathematical technique, mainly the theory of analytical functions, from scratch.



Fractured Rock Hydraulics

Fractured Rock Hydraulics Author Fernando Olavo Franciss
ISBN-10 9781439859155
Release 2009-12-28
Pages 188
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Uniquely devoted to hard and fractured rock hydraulics, this advanced-level introduction provides tools to solve practical engineering problems. Chapter I covers the fundamentals of fractured rock hydraulics under a tensor approach. Chapter II presents some key concepts about approximate solutions. Chapter III discuss a few data analysis techniques applied to groundwater modeling. Chapter IV presents unique 3D finite difference algorithms to simulate practical problems concerning the hydraulic behavior of saturated, heterogeneous and randomly fractured rock masses without restriction to the geometry and properties of their discontinuities. Supported by examples, cases, illustrations and references, this book is intended for professionals and researchers in hydrogeology, engineering geology, petroleum reservoir, rock and hydraulic engineering. Its explanatory nature allows its use as a textbook for advanced students.



Engineering Analysis with ANSYS Software

Engineering Analysis with ANSYS Software Author Tadeusz Stolarski
ISBN-10 9780081021651
Release 2018-01-10
Pages 562
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Engineering Analysis with ANSYS Software, Second Edition, provides a comprehensive introduction to fundamental areas of engineering analysis needed for research or commercial engineering projects. The book introduces the principles of the finite element method, presents an overview of ANSYS technologies, then covers key application areas in detail. This new edition updates the latest version of ANSYS, describes how to use FLUENT for CFD FEA, and includes more worked examples. With detailed step-by-step explanations and sample problems, this book develops the reader’s understanding of FEA and their ability to use ANSYS software tools to solve a range of analysis problems. Uses detailed and clear step-by-step instructions, worked examples and screen-by-screen illustrative problems to reinforce learning Updates the latest version of ANSYS, using FLUENT instead of FLOWTRAN Includes instructions for use of WORKBENCH Features additional worked examples to show engineering analysis in a broader range of practical engineering applications



Variational Analysis in Sobolev and BV Spaces

Variational Analysis in Sobolev and BV Spaces Author Giuseppe Buttazzo
ISBN-10 0898718783
Release 2006
Pages 634
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This self-contained book is excellent for graduate-level courses devoted to variational analysis, optimization, and partial differential equations (PDEs). It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. It contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references. The book is divided into two parts. In Part I, classical Sobolev spaces are introduced and the reader is provided with the basic tools and methods of variational analysis and optimization in infinite dimensional spaces, with applications to classical PDE problems. In Part II, BV spaces are introduced and new trends in variational analysis are presented.



The Thermomechanics of Plasticity and Fracture

The Thermomechanics of Plasticity and Fracture Author Gerard A. Maugin
ISBN-10 0521397804
Release 1992-05-21
Pages 350
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This book concentrates upon the mathematical theory of plasticity and fracture as opposed to the physical theory of these fields, presented in the thermomechanical framework.



Practical Fracture Mechanics in Design

Practical Fracture Mechanics in Design Author Arun Shukla
ISBN-10 9780849338939
Release 2004-12-14
Pages 522
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Theoretical treatments of fracture mechanics abound in the literature. Among the first books to address this vital topic from an applied standpoint was the first edition of Practical Fracture Mechanics in Design. Completely updated and expanded to reflect recent developments in the field, the second edition of this valuable reference concisely reviews all of the fracture modes and design methodologies needed for control and prevention of structural failures in mechanical components. Practical Fracture Mechanics in Design, Second Edition begins with the historical development of the field, which is critical in understanding the origins and purpose of the various methodologies and equations. The book goes on to provide the fundamentals, basic formulas, elementary worked examples, and references with an emphasis on linear elastic fracture mechanics (LEFM). The author also includes case studies and design problems to clarify the concepts and explain their application. New chapters cover experimental methods in fracture, fracture of composite materials, dynamic fracture, and post mortem analysis of fracture surfaces. Providing much more than a simple introduction to fracture mechanics, this critical, authoritative guide supplies easy-to-use and understand tools based on hands-on experience in design, emphasizing practical applications over heavily theoretical, rigorous mathematical derivations.



Micromechanics of Fracture in Generalized Spaces

Micromechanics of Fracture in Generalized Spaces Author Ihar Alaksandravich Miklashevich
ISBN-10 0080556752
Release 2008-01-08
Pages 280
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By the detailed analysis of the modern development of the mechanics of deformable media can be found the deep internal contradiction. From the one hand it is declared that the deformation and fracture are the hierarchical processes which are linked and unite several structural and scale levels. From the other hand the sequential investigation of the hierarchy of the deformation and destruction is not carried out. The book’s aim is filling this mentioned gap and investigates the hot topic of the fracture of non-ideal media. From the microscopic point of view in the book we study the hierarchy of the processes in fractured solid in the whole diapason of practically used scales. According the multilevel hierarchical system ideology under “microscopic we understand taking into account the processes on the level lower than relative present strata. From hierarchical point of view the conception of “microscopic fracture can be soundly applied to the traditionally macroscopic area, namely geomechanics or main crack propagation. At the same time microscopic fracture of the nanomaterials can be well-grounded too. This ground demands the investigation on the level of inter-atomic interaction and quantum mechanical description. The important feature of the book is the application of fibred manifolds and non-Euclidean spaces to the description of the processes of deformation and fracture in inhomogeneous and defected continua. The non-Euclidean spaces for the dislocations’ description were introduced by J.F. Nye, B.A. Bilby, E. Kröner, K. Kondo in fiftieth. In last decades this necessity was shown in geomechanics and theory of seismic signal propagation. The applications of non-Euclidean spaces to the plasticity allow us to construct the mathematically satisfying description of the processes. Taking into account this space expansion the media with microstructure are understood as Finsler space media. The bundle space technique is used for the description of the influence of microstructure on the continuum metrics. The crack propagation is studied as a process of movement in Finsler space. Reduction of the general description to the variational principle in engineering case is investigated and a new result for the crack trajectory in inhomogeneous media is obtained. Stability and stochastization of crack trajectory in layered composites is investigated. The gauge field is introduced on the basis of the structure representation of Lie group generated by defects without any additional assumption. Effective elastic and non-elastic media for nanomaterials and their geometrical description are discussed. The monograph provides the basis for more detailed and exact description of real processes in the material. The monograph will be interesting for the researchers in the field of fracture mechanics, solid state physics and geomechanics. It can be used as well by the last year students wishing to become more familiar with some modern approaches to the physics of fracture and continual theory of dislocations. In Supplement, written by V.V.Barkaline, quantum mechanical concept of physical body wholeness according to H. Primas is discussed with relation to fracture. Role of electronic subsystem in fracture dynamics in adiabatic and non-adiabatic approximations is clarified. Potential energy surface of ion subsystem accounting electron contribution is interpreted as master parameter of fracture dynamics. Its features and relation to non-euclidean metrics of defected solid body is discussed. Quantum mechanical criteria of fracture arising are proposed.