Inverse and crack identification problems are of paramount importance for health monitoring and quality control purposes arising in critical applications in civil, aeronautical, nuclear, and general mechanical engineering. Mathematical modeling and the numerical study of these problems require high competence in computational mechanics and applied optimization. This is the first monograph which provides the reader with all the necessary information. Delicate computational mechanics modeling, including nonsmooth unilateral contact effects, is done using boundary element techniques, which have a certain advantage for the construction of parametrized mechanical models. Both elastostatic and harmonic or transient dynamic problems are considered. The inverse problems are formulated as output error minimization problems and they are theoretically studied as a bilevel optimization problem, also known as a mathematical problem with equilibrium constraints. Beyond classical numerical optimization, soft computing tools (neural networks and genetic algorithms) and filter algorithms are used for the numerical solution. The book provides all the required material for the mathematical and numerical modeling of crack identification testing procedures in statics and dynamics and includes several thoroughly discussed applications, for example, the impact-echo nondestructive evaluation technique. Audience: The book will be of interest to structural and mechanical engineers involved in nondestructive testing and quality control projects as well as to research engineers and applied mathematicians who study and solve related inverse problems. People working on applied optimization and soft computing will find interesting problems to apply to their methods and all necessary material to continue research in this field.

The 4th International Conference on Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials was held from 7-11 September 1998 in Garmisch-Partenkirchen, Germany.

In response to a call for papers, nearly 200 extended abstracts from 32 countries were submitted to the organizing committee. These papers were presented at the conference as invited lectures or short contributions and as oral or poster presentation. All the papers were presented in poster form in extended poster sessions a peculiarity of the LCF Conferences which allows an intense, thorough discussion of all contributions.

Each chapter provides a comprehensive overview of a materials class or a given subject. Many contributions could have been included in two or even three chapters and so, in order to give a better overview of the content, the reader will find a subject index, a material index and an author index in the back of the book.
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This book introduces recent theoretical developments concerning the dynamic behaviour of fracture. Readers learn how the recent development of molecular dynamics and other state-of-the-art methods can help to solve the important problem of fracture from the atomic level.

In the preliminary stage of designing new structural hardware that must perform a given mission in a fluctuating load environment, there are several factors the designers should consider. Trade studies for different design configurations should be performed and, based on strength and weight considerations, among others, an optimum configuration selected. The selected design must be able to withstand the environment in question without failure. Therefore, a comprehen sive structural analysis that consists of static, dynamic, fatigue, and fracture is necessary to ensure the integrity of the structure. During the past few decades, fracture mechanics has become a necessary discipline for the solution of many structural problems. These problems include the prevention of failures resulting from preexisting cracks in the parent material, welds or that develop under cyclic loading environment during the life of the structure. The importance of fatigue and fracture in nuclear, pressure vessel, aircraft, and aerospace structural hardware cannot be overemphasized where safety is of utmost concern. This book is written for the designer and strength analyst, as well as for the material and process engineer who is concerned with the integrity of the structural hardware under load-varying environments in which fatigue and frac ture must be given special attention. The book is a result of years of both acade mic and industrial experiences that the principal author and co-authors have accumulated through their work with aircraft and aerospace structures."

This Volume constitutes the Proceedings of the IUTAM Symposium on 'Scaling Laws in Ice Mechanics and Ice Dynamics', held in Fairbanks, Alaska from 13th to 16th of June 2000. Ice mechanics deals with essentially intact ice: in this discipline, descriptions of the motion and deformation of Arctic/ Antarctic and river/lake ice call for the development of physically based constitutive and fracture models over an enormous range in scale: 0.01 m - 10 km. Ice dynamics, on the other hand, deals with the movement of broken ice: descriptions of an aggregate of ice floes call for accurate modeling of momentum transfer through the sea/ice system, again over an enormous range in scale: 1 km (floe scale) - 500 km (basin scale). For ice mechanics, the emphasis on lab-scale (0.01 - 0.5 m) research con trasts with applications at the scale of order 1 km (ice-structure interaction, icebreaking); many important upscaling questions remain to be explored.

In this book, a new phenomenological approach to brittle medium fractu re initiation under shock pulses is developed. It provides an opportun ity to estimate fracture of media with and without macrodefects. A qua litative explanation is thus obtained for a number of principally impo rtant effects of high-speed dynamic fracture that cannot be clarified within the framework of previous approaches. It is possible to apply t his new strategy to resolve applied problems of disintegration, erosio n, and dynamic strength determination of structural materials. Special ists can use the methods described to determine critical characteristi cs of dynamic strength and optimal effective fracture conditions for r igid bodies. This book can also be used as a special educational cours e on deformation of materials and constructions, and fracture mechanic s.

In recent times, the use of composites and functionally graded materials (FGMs) in structural applications has increased. FGMs allow the user to design materials for a specified functionality and therefore have numerous uses in structural engineering. However, the behaviour of these structures under high-impact loading is not well understood. Spectral Finite Element Method: Wave Propagation, Health Monitoring and Control in Composite and Functionally Graded Structures focuses on some of the wave propagation and transient dynamics problems with this complex media which had previously been thought unmanageable.

By using state-off-the-art computational power, the Spectral Finite Element Method (SFEM) can solve many practical engineering problems. This book is the first to apply SFEM to inhomogeneous and anisotropic structures in a unified and systematic manner. The authors discuss the different types of SFEM for regular and damaged 1-D and 2-D waveguides, various solution techniques, different methods of detecting the presence of damages and their locations, and different methods available to actively control the wave propagation responses. The theory is supported by tables, figures and graphs; all the numerical examples are so designed to bring out the essential wave behaviour in these complex structures. Some case studies based on real-world problems are also presented.

This book is intended for senior undergraduate students and graduate students studying wave propagation in structures, smart structures, spectral finite element method and structural health monitoring. Readers will gain a complete understanding of how to formulate a spectral finite element; learn about wavebehaviour in inhomogeneous and anisotropic media; and, discover how to design some diagnostic tools for monitoring the health or integrity of a structure. This important contribution to the engineering mechanics research community will also be of value to researchers and practicing engineers in structural integrity.

This is the fourth volume in the well-established series of compendiums devoted to the subject of weld hot cracking. It contains the papers presented at the 4th International Cracking Workshop held in Berlin in April 2014. In the context of this workshop, the term "cracking" refers to hot cracking in the classical and previous sense, but also to cold cracking, stress-corrosion cracking and elevated temp. solid-state cracking. A variety of different cracking subjects are discussed, including test standards, crack prediction, weldability determination, crack mitigation, stress states, numerical modelling, and cracking mechanisms. Likewise, many different alloys were investigated such as aluminum alloys, copper-aluminum dissimilar metal, austenitic stainless steel, nickel base alloys, duplex stainless steel, creep resistant steel, and high strength steel.

This book describes and discusses the properties of heterogeneous materials. The properties considered include the conductivity (thermal, electrical, magnetic), elastic moduli, dielectrical constant, optical properties, mechanical fracture, and electrical and dielectrical breakdown properties. Both linear and nonlinear properties are considered. The nonlinear properties include those with constitutive non-linearities as well as threshold non-linearities, such as brittle fracture and dielectric breakdown. A main goal of this book is to compare two fundamental approaches to describing and predicting materials properties, namely, the continuum mechanics approach, and those based on the discrete models. The latter models include the lattice models and the atomistic approaches. The book provides comprehensive and up to date theoretical and computer simulation analysis of materials' properties. Typical experimental methods for measuring all of these properties are outlined, and comparison is made between the experimental data and the theoretical predictions. Volume I covers linear properties, while Volume II considers non-linear and fracture and breakdown properties, as well as atomistic modeling. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.

The book comprises the 3rd collection of benchmarks and examples for porous and fractured media mechanics. Analysis of thermo-hydro-mechanical-chemical (THMC) processes is essential to a wide area of applications in environmental engineering, such as geological waste deposition, geothermal energy utilization (shallow and deep systems), carbon capture and storage (CCS) as well as water resources management and hydrology. In order to assess the feasibility, safety as well as sustainability of geoenvironmental applications, model-based simulation is the only way to quantify future scenarios. This charges a huge responsibility concerning the reliability of conceptual models and computational tools. Benchmarking is an appropriate methodology to verify the quality and validate the concept of models based on best practices. Moreover, benchmarking and code comparison are building strong community links. The 3rd THMC benchmark book also introduces benchmark-based tutorials, therefore the subtitle is selected as "From Benchmarking to Tutoring". The benchmark book is part of the OpenGeoSys initiative - an open source project to share knowledge and experience in environmental analysis and scientific computation. The new version of OGS-6 is introduced and first benchmarks are presented therein (see appendices).

This volume contains 18 papers selected from 90 presented at the Fifth International Conference on Biaxial/Multiaxial Fatigue and Fracture held in Cracow, Poland 8-12 September 1997. The papers in this book deal with theoretical, computational and experimental aspects of the multiaxial fatigue and fracture of engineering materials and structures. The papers are divided into the following four categories:
1. Proportional cyclic loading
2. Non-proportional cyclic loading
3. Variable amplitude and random loading
4. Crack growth

Most papers in this publication talk about the behaviour of constructional materials and elements of machines under non-proportional loading and under variable amplitude and random loading, which are more realistic load histories met in industrial practice. Variable amplitude loading under cyclic load with basic frequency and random loading under load with a continuous band of frequency is classified here. This book gives a review of the latest world success and directions of investigations on multiaxial fatigue and fracture. More and more often publications are results of the co-operation of researchers from different laboratories and countries. Seven out of eighteen papers included here were worked out by international authors teams. This is a symptom of the times, when science and investigations know no borders.

On Fracture Mechanics A major objective of engineering design is the determination of the geometry and dimensions of machine or structural elements and the selection of material in such a way that the elements perform their operating function in an efficient, safe and economic manner. For this reason the results of stress analysis are coupled with an appropriate failure criterion. Traditional failure criteria based on maximum stress, strain or energy density cannot adequately explain many structural failures that occurred at stress levels considerably lower than the ultimate strength of the material. On the other hand, experiments performed by Griffith in 1921 on glass fibers led to the conclusion that the strength of real materials is much smaller, typically by two orders of magnitude, than the theoretical strength. The discipline of fracture mechanics has been created in an effort to explain these phenomena. It is based on the realistic assumption that all materials contain crack-like defects from which failure initiates. Defects can exist in a material due to its composition, as second-phase particles, debonds in composites, etc. , they can be introduced into a structure during fabrication, as welds, or can be created during the service life of a component like fatigue, environment-assisted or creep cracks. Fracture mechanics studies the loading-bearing capacity of structures in the presence of initial defects. A dominant crack is usually assumed to exist.

The assessment of crack initiation and/or propagation has been the subject of many past discussions on fracture mechanics. Depending on how the chosen failure criterion is combined with the solution of a particular theory of continuum mechanics, the outcome could vary over a wide range. Mod elling of the material damage process could be elusive if the scale level of observation is left undefined. The specification of physical dimension alone is not sufficient because time and temperature also play an intimate role. It is only when the latter two variables are fixed that failure predictions can be simplified. The sudden fracture of material with a pre-existing crack is a case in point. Barring changes in the local temperature,* the energy released to create a unit surface area of an existing crack can be obtained by considering the change in elastic energy of the system before and after crack extension. Such a quantity has been referred to as the critical energy release rate, G e, or stress intensity factor, K Ie. Other parameters, such as the crack opening displacement (COD), path-independent J-integral, etc. , have been proposed; their relation to the fracture process is also based on the energy release concept. These one-parameter approaches, however, are unable simultaneously to account for the failure process of crack initiation, propagation and onset of rapid fracture. A review on the use of G, K I, COD, J, etc. , has been made by Sih [1,2].

- self-contained and well illustrated

- complete and comprehensive derivation of mechanical/mathematical results with enphasis on issues of practical importance

- combines classical subjects of fracture mechanics with modern topics such as microheterogeneous materials, piezoelectric materials, thin films, damage

- mechanically and mathematically clear and complete derivations of results

Proceedings of First USA-Greece Symposium on Mixed Mode Crack Propagation, Athens, Greece, 18-22 August, 1980

The purpose of this book is to present, describe and demonstrate the use of numerical methods in solving crack problems in fracture mechanics. The text concentrates, to a large extent, on the application of the Boundary Element Method (BEM) to fracture mechanics, although an up-to-date account of recent advances in other numerical methods such as the Finite Element Method is also presented. The book is an integrated presentation of modem numerical fracture mechanics, it contains a compilation of the work of many researchers as well as accounting for some of authors' most recent work on the subject. It is hoped that this book will bridge the gap that exists between specialist books on theoretical fracture mechanics on one hand, and texts on numerical methods on the other. Although most of the methods presented are the latest developments in the field of numerical fracture mechanics, the authors have also included some simple techniques which are essential for understanding the physical principles that govern crack problems in general. Different numerical techniques are described in detail and where possible simple examples are included, as well as test results for more complicated problems. The book consists of six chapters. The first chapter initially describes the historical development of theoretical fracture mechanics, before proceeding to present the basic concepts such as energy balance, stress intensity factors, residual strength and fatigue crack growth as well as briefly describing the importance of stress intensity factors in corrosion and residual stress cracking.

This International Conference on Analytical and Experimental Fracture Me chanics was organized jointly by the Centro Sperimentale Metallurgico, S. p. A. , Lehigh University and Italsider S. p. A. It took place at the Hotel Midas Palace in Rome, Italy, during 23-27 June, 1980. There were more than 150 attendees from 19 different countries: Australia, Austria, Belgium, Canada, People's Re public of China, Czechoslovakia, Finland, Federal Republic of Germany, Hungary, Israel, Italy, Japan, The Netherlands, Poland, Switzerland, Turkey, UK, USA and USSR. Dr. G. M. Costa from Finsider officially opened the Conference and gave the Welcome Address. More than 70 technical papers were presented at three con current sessions. There were six plenary lectures that helped to integrate the diverse efforts, e. g. , analytical fracture mechanics, testing methods, metallur gical effects, corrosion fatigue, dynamic crack propagation and weldments of in dividual researchers. In addition to providing an overall view of the current status of fracture mechanics technology, particular emphasis was given to methods of controlling fracture in gas pipeline structures. The members of the Organizing Committee made a special effort to organize a panel discussion on the application of fracture mechanics technology to the safe design of large diameter pipelines. Dr. Michele Civallero from Italsider and Professor George C. Sih from Lehigh University served as panel Co-Chairmen and delivered survey lectures to stimulate questions from the audience.

From time to time the International Journal of Fracture has presented matters thought to be of special interest to its readers. In previous special issues (December 1980 and April 1981), Dr H.W. Liu as Guest Editor presented a series of review papers dealing with fatigue processes and characteristics in metals and non-metals. Continuing this policy, which is consistent with our stated objectives, a second review dealing with time depen dence in the fracture process, including the effect of material inertia but essentially excluding very strong shock effects in solids, has been assembled under the generic term "dynamic fracture." We hope that the ensuing state-of-the-art review will yield an instructive and timely product which readers will find useful. To assist us in presenting this subject, we have prevailed upon a well-known worker in dynamic fracture, Dr W.G. Knauss, Professor of Aeronautics and Applied Mechanics, California Institute of Technology to act as Guest Editor for this special double issue. On behalf of the editors and publisher, I wish to express our indebtedness to Professor Knauss and his invited authors for undertaking this special effort."

Failures of many mechanical components in service result from fatigue. The cracks which grow may either originate from some pre-existing macroscopic defect, or, if the component is of high integrity but highly stressed, a region of localized stress concentration. In turn, such concentrators may be caused by some minute defect, such as a tiny inclusion, or inadvertent machining damage. Another source of surface damage which may exist between notionally 'bonded' components is associated with minute relative motion along the interface, brought about usually be cyclic tangential loading. Such fretting damage is quite insidious, and may lead to many kinds of problems such as wear, but it is its influence on the promotion of embryo cracks with which we are concerned here. When the presence of fretting is associated with decreased fatigue performance the effect is known as fretting fatigue. Fretting fatigue is a subject drawing equally on materials science and applied mechanics, but it is the intention in this book to concentrate attention entirely on the latter aspects, in a search for the quantification of the influence of fretting on both crack nucleation and propagation. There have been very few previous texts in this area, and the present volume seeks to cover five principal areas; (a) The modelling of contact problems including partial slip under tangentialloading, which produces the surface damage. (b) The modelling of short cracks by rigorous methods which deal effectively with steep stress gradients, kinking and closure. (c) The experimental simulation of fretting fatigue.

For a brief period during the latter part of World War II, Nevill F. Mott led a theoretical group at Fort Halstead in the United Kingdom that tackled scientific issues related to pressing war-time concerns. Among later awards and honors, Mott was knighted and a recipient of the Nobel Prize. While at Fort Halstead, he undertook an effort to theoretically describe the statistical fragmentation of munitions subjected to intense explosive loading. Mott`s original internal reports contain seminal theoretical concepts on the physics and statistics of dynamic fracture and fragmentation, which have provided the inspiration for numerous later modeling efforts and engineering formulae. Some of his most forward-looking thoughts on the micromechanical and molecular aspects of fracture are included in these publications. The present book surveys the theoretical analysis put forth by Mott with particular focus on his efforts to characterize the size and distribution of fragments resulting from a dynamic fragmentation event. Copies of the original internal reports of Mott and his co-workers are included. The book also pursues additional theoretical analysis with the intent of delving further into the physical ideas and unfinished analysis implicit in Mott`s original studies. This book will be of interest to all scientists and engineers concerned with the dynamic fracture and fragmentation of solid bodies subject to intense transient loads imparted by explosive detonation and high-velocity impact from both the historical and modern perspective.

From time to time the International Journal of Fracture has presented matters thought to be of special interest to its readers. The last special topic review was presented by Drs W.G. Knauss and AJ. Rosakis as Guest Editors in four issues, January-April 1990, under the general title of Non Linear Fracture. It contained sections on damage mechanisms, interfaces and creep, time depen dence, and continuum plasticity insofar as they affect the mechanisms of the fracture process. Continuing this policy, which is consistent with our stated objectives, the two September issues deal with the behavior of concrete and cementious materials during fracture initiation and propagation. We hope that the ensuing state-of-the-art review will yield another instructive and timely product which readers will find useful. To assist us in presenting this subject, we have prevailed upon a well-known international expert in concrete behavior, Dr. Z.P. Bazant, Walter P. Murphy Professor of Civil Engineering, of Northwes tern University to act as Guest Editor. On behalf of the editors and publishers, I wish to thank Professor BaZant and his invited authors for undertaking this special effort. M.L. WILLIAMS Pittsburgh, Pennsylvania Editor-in-Chief September 1991 International Journal of Fracture 51: ix-xv, 1991. Z.P. Bafant (ed.), Current Trends in Concrete Fracture Research.

The main scope of this Cargese NATO Advanced Study Institute (June 5-17 2000) was to bring together a number of international experts, covering a large spectrum of the various Physical Aspects of Fracture. As a matter of fact, lecturers as well as participants were coming from various scientific communities: mechanics, physics, materials science, with the common objective of progressing towards a multi-scale description of fracture. This volume includes papers on most materials of practical interest: from concrete to ceramics through metallic alloys, glasses, polymers and composite materials. The classical fields of damage and fracture mechanisms are addressed (critical and sub-critical quasi-static crack propagation, stress corrosion, fatigue, fatigue-corrosion . . . . as well as dynamic fracture). Brittle and ductile fractures are considered and a balance has been carefully kept between experiments, simulations and theoretical models, and between the contributions of the various communities. New topics in damage and fracture mechanics - the effect of disorder and statistical aspects, dynamic fracture, friction and fracture of interfaces - were also explored. This large overview on the Physical Aspects of Fracture shows that the old barriers built between the different scales will soon "fracture." It is no more unrealistic to imagine that a crack initiated through a molecular dynamics description could be propagated at the grain level thanks to dislocation dynamics included in a crystal plasticity model, itself implemented in a finite element code. Linking what happens at the atomic scale to fracture of structures as large as a dam is the new emerging challenge.

In this volume a survey of the most relevant nonlinear crack models is provided, with the purpose of analyzing the nonlinear mechanical effects occurring at the tip of macrocracks in quasi-brittle materials - such as concrete, rocks, ceramics, polymers, high-strength metallic alloys - and in brittle-matrix fibre-reinforced composites. Such local effects, as, for example, plastic deformation, yielding, strain-hardening, strain-softening, mechanical damage, matrix microcracking, aggregate debonding, fibre bridging, fibre slippage, crazing, and so on, are properly described through different simplified models, representing the peculiarities of the phenomena involved. The models are introduced and described separately and then compared in the last part of the book. This volume will be of interest to students, professionals and researchers in the field of nonlinear fracture mechanics.

Today, Fracture Mechanics is a well known topic within the scientific community. Applications of Fracture Mechanics can be found in various fields ranging from solid mechanics and structures to materials sciences and computational mechanics. However, most of these results apply only to linear fracture mechanics of two-dimensional and homogeneous isotropic solids. Therefore there are still incompletely solved problems; such as non-linearity, frictional contact cracks, residual stresses in fracture mechanics, three-dimensional crack geometry, coupled cracked solid/fluid, etc. Recently, new topics related to crack detection based on different physical phenomena have appeared.

This book is an attempt to present, in a unified manner, different topics of Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to under-graduate students. These new topics take into consideration the thermodynamics of continuous media, including thermal and dynamical aspects. In addition, the book introduces the notion of duality or symmetry in Solids Mechanics. The loss of symmetry is exploited to provide a unique and powerful tool, called the reciprocity gap functional introduced by the authora (TM)s groups, to solve explicitly some important inverse problems arising in crack determination as well as in the earthquake inverse problem.

With its emphasis, initially on physical or experimental back-grounds, and then on analysis and theoretical results, rather than on numerical computations, this monograph is intended to beused by students and researchers in solids mechanics, mechanical engineering and applied mathematics.

As Directors of this NATO Workshop, we welcome this opportunity to record formally our thanks to the NATO Scientific Affairs Division for making our meeting possible through generous financial support and encouragement. This meeting has two purposes: the first obvious one because we have collected scientists from East, far East and west to discuss new development in the field of fracture mechanics: the notch fracture mechanics. The second is less obvious but perhaps in longer term more important that is the building of bridges between scientists in the frame of a network called Without Walls Institute on Notch Effects in Fatigue and Fracture." Physical perception of notch effects is not so easy to understand as the presence of a geometrical discontinuity as a worst effect than the simple reduction of cross section. Notch effects in fatigue and fracture is characterised by the following fundamental fact: it is not the maximum local stress or stress which governs the phenomena of fatigue and fracture. The physic shows that a process volume is needed probably to store the necessary energy for starting and propagating the phenomenon. This is a rupture of the traditional "strength of material" school which always give the prior importance of the local maximum stress. This concept of process volume was strongly affirmed during this workshop.