Computational mechanics, as a science employed for the numerical model ing of processes in nature and engineering, has over the last few decades developed two strands. The first concerns the putting of more and more powerful software packages into computational practice, using increas ingly high-performance computers with increasingly large memory. The traditional finite element and finite difference approaches are still preva lent. Over the years however, researchers have met with new problems; their solutions on the basis of traditional methods are at best difficult and at worst impossible to obtain. Such problems provided a powerful impetus in the development of the second strand, resulting in the development of es sentially new approaches for numerical modeling, for example meshless methods, "molecular" dynamics, neuron networks. The current state of the art formed the basis of many papers presented at the Fifth World Congress on Computational Mechanics, Vienna 2002. It is within the framework of the second strand that this book has been written."

As one of the oldest natural sciences, mechanics occupies a certain pioneering role in determining the development of exact sciences through its interaction with mathematics. As a matter of fact, there is hardly an area in mathematics that hasn't found an application of some form in mechanics. It is thus almost inevitable that theoretical methods in mechanics are highly developed and laid out on different levels of abstraction. With the spread of digital processors this goes as far as the implementation in commercial computer codes, where the user is merely con fronted on the surface with the processes that run in the background, i. e. mechan ics as such: in teaching and research, as well as in the context of industry, me chanics is much more, and must remain much more than the mere production of data with the help of a processor. Mechanics, as it is talked about here, tradition ally includes a wide spectrum, ranging from applied mechanics, analytical and technical mechanics to modeling. and experimental mechanics, as well as technical realization. It also includes the subdisciplines of rigid body mechanics, continuum mechanics, or fluid mechanics, to mention only a few. One of the fundamental and most important concepts used by nearly all natural sciences is the concept of linearization, which assumes the differentiability of mappings. As a matter of fact, all of classical mechanics is based on the avail ability of this quality."

The book deals with atomistic properties of solids which are determined by the crystal structure, interatomic forces and atomic displacements influenced by the effects of temperature, stress and electric fields. The book gives equal importance to experimental details and theory. There are full chapters dedicated to the tensor nature of physical properties, mechanical properties, lattice vibrations, crystal structure determination and ferroelectricity. The other crystalline states like nano-, poly-, liquid- and quasi crystals are discussed. Several new topics like nonlinear optics and the Rietveld method are presented in the book. The book lays emphasis on the role of symmetry in crystal properties. Comprehensiveness is the strength of the book; this allows users at different levels a choice of chapters according to their requirements.

Plate structures are used in almost every area of engineering, including aerospace and naval architecture, civil engineering, and electronics. These structures have diverse geometries and have to withstand a wide range of loading conditions. This book provides the theoretical foundations of the theories of plates manufactured from various materials, outlines and illustrates the methods used for the analysis of these structures, and emphasizes designs and solution techniques available to an engineer. The book is written for engineers working in industry, graduate students at aerospace, mechanical, civil engineering and naval architecture departments, and investigators interested in the development of the theory of plates and related subjects. While the mathematical modeling employed in the book is understandable to both engineers and graduate students, the book also provides insight into relevant phenomena and theories underlying plate structures. Thus, the reader is equipped with a thorough understanding of the problems and appropriate assumptions, even if the analysis is conducted using commercially available software codes. In addition, the book includes numerous analytical solutions that can confidently be used in the design of plate structures. The combination of theoretical insight and references to practical problems makes the book equally attractive to academia and industry.

At the VIIth International Congress on Rheology, which was held in Goteborg in 1976, Proceedings were for the first time printed in advance and distributed to all participants at the time of the Congress. Although of course we Italians would be foolish to even try to emulate our Swedish friends as far as efficiency of organization is concerned, we decided at the very beginning that, as far as the Proceedings were concerned, the VIIIth International Congress on Rheology in Naples would follow the standards of time liness set by the Swedish Society of Rheology. This book is the result we have obtained. We wish to acknowledge the cooperation of Plenum Press in producing it within the very tight time schedule available. Every four years, the International Congress on Rheology represents the focal point where all rheologists meet, and the state of the art is brought up to date for everybody interested; the Proceedings represent the written record of these milestones of scientific progress in rheology. We have tried to make use of the traditions of having invited lectures, and of leaving to the organizing committee the freedom to choose the lecturers as they see fit, in order to collect a group of invited lectures which gives as broad as possible a landscape of the state of the art in every relevant area of rheology. The seventeen invited lectures are collected in the first volume of the proceedings."

Written for researchers and advanced students the book exhibits a combination of various methods and tools required to describe the complexity of the chemical and physical behaviour of fluid surfaces. The common denominator for all the contributions presented here is the simultaneous use of concepts from surface chemistry and physics and from hydrodynamics where external force fields can be introduced. Theoretical and experimental work is equally represented. Most of the basic problems in the area of nonequilibrium multiphase systems have not yet received extensive treatment. This volume should be a reference for physicists, physico-chemists, and chemical engineers and will serve as a jumping-off point for new directions and new points of view.

This book covers a wide area of topics, from fundamental theories to industrial applications. It serves as a useful reference for everyone interested in computational modeling of partial differential equations pertinent primarily to aeronautical applications. The reader will find three survey articles on the present state of the art in numerical simulation of the transition to turbulence, in design optimization of aircraft configurations, and in turbulence modeling. These are followed by carefully selected and refereed articles on algorithms and their applications, on design methods, on grid adaption techniques, on direct numerical simulations, and on parallel computing, and much more.

A straightforward introduction to basic concepts and methodologies for digital photoelasticity, providing a foundation on which future researchers and students can develop their own ideas. The book thus promotes research into the formulation of problems in digital photoelasticity and the application of these techniques to industries. In one volume it provides data acquisition by DIP techniques, its analysis by statistical techniques, and its presentation by computer graphics plus the use of rapid prototyping technologies to speed up the entire process. The book not only presents the various techniques but also provides the relevant time-tested software codes. Exercises designed to support and extend the treatment are found at the end of each chapter.

Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models.
The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.

My wife Tatyana, daughter Mariya, son Alexandr It is well known that the mixed-mode conditions appear when the direction of the applied loading does not coincide with the orthogonal K, -Kn-Km space. In general, in the industrial practice the mixed-mode fracture and the mixed-mode crack growth are more likely to be considered the rule than the exception. Miller et al. considers that cracks can grow due to a mixture of processes (ductile and brittle), mechanisms (static, fatigue, creep) and loading modes (tension, torsion, biax ial/multiaxial). Additionally mixed-mode crack-extension can be affected by many other considerations such as artifact geometry (thin plates, thick shells, and the size, shape and orientation of the defect), environmental effects (temperature, gaseous and liquid surroundings), material state (crystallographic structure, heat treatment and route of manufacture) and stress conditions (out-of-phase and ran dom loading effects). The main feature of the mixed-mode fracture is that the crack growth would no longer take place in a self-similar manner and does not follow a universal trajec tory that is it will grow on a curvilinear path. There are various fracture criteria, which predict the behavior of cracks in brittle and ductile materials loaded in combined modes. Linear elastic fracture mechanics (LEFM) criteria predict basi cally the same direction for crack propagation. Cracks in brittle materials have been shown to propagate normal to the maximum tangential stress. In ductile ma terials yielding occurs at the crack tip and LEFM is no longer applicable."

The volume is devoted to mechanics of rods, which is a branch of mechanics of deformable bodies. The main goal of the book is to present systematically theoretical fundamentals of mechanics of rods as well as numerical methods used for practical purposes. The monograph is concerned with the most general statements of the problems in mechanics of rods. Various types of external loads that a rod may be subject to are discussed. Advanced technique that includes vector is used in the derivation of linear analysis, linear algebra, and distributions and nonlinear equilibrium equations. The use of this technique helps us to make transformations and rearrangement of equations more transparent and compact. Theoretical basics of rods interacting with external and internal flows of fluid and the derivation of the formulas for the hydrodynamic and aerody namic forces are presented. The book consists of six chapters and appendices and may be convention ally divided into two parts. That is, Chapters 1 to 3 contain, in the main, theoretical material, whereas Chapters 4 to6 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 1, 3, 4, and 5. The solutions to most of the problems are given in Appendix B. The monograph is addressed to scientists, institutional and industrial re searchers, lecturers, and graduate students."

The objective of this book is to provide a comprehensive introduction to ?nite rotation shells and to non-linear shell ?nite elements. It is divided into 5 parts: I. Preliminaries (20 pages), II. Shell equations (104 pages), III. Finite rotations for shells (103 pages), IV. Four-node shell elements (189 pages), and V. Numerical examples (41 pages). Additional numerical examples are presented in Parts III and IV. The bibliography includes 270 entries. The book is intended for both teaching and self-study, and emphasizes fundamental aspects and techniques of the subject. Some familiarity with non-linear mechanics and the ?nite element method is assumed. Shell elements are a subject of active research which results in many publications every year and several conferences and sessions are held r- ularly, among them, two large international conferences: \Computation of Shell and Spatial Structures" and \Shell Structures. Theory and - plications" (SSTA). The literature is voluminous, not easy to follow and evaluate, and the subject is di-cult to comprehend. I hope that this will be facilitated by the book. I would like to express my gratitude to several persons who helped me in my professional life, in this way contributing to the book. I thank Prof. R.L. Taylor from the University of California at Berkeley, Prof. B. Schre er from the University of Padua, and Prof. J.T. Santos from the Instituto Superior Tecnico at Lisbon, for hosting and supporting me when I was a post-doctoral researcher.

The last decades have witnessed the development of methods for solving struc tural reliability problems, which emerged from the efforts of numerous re searchers all over the world. For the specific and most common problem of determining the probability of failure of a structural system in which the limit state function g( x) = 0 is only implicitly known, the proposed methods can be grouped into two main categories: * Methods based on the Taylor expansion of the performance function g(x) about the most likely failure point (the design point), which is determined in the solution process. These methods are known as FORM and SORM (First- and Second Order Reliability Methods, respectively). * Monte Carlo methods, which require repeated calls of the numerical (nor mally finite element) solver of the structural model using a random real ization of the basic variable set x each time. In the first category of methods only SORM can be considered of a wide applicability. However, it requires the knowledge of the first and second deriva tives of the performance function, whose calculation in several dimensions either implies a high computational effort when faced with finite difference techniques or special programs when using perturbation techniques, which nevertheless require the use of large matrices in their computations. In or der to simplify this task, use has been proposed of techniques that can be regarded as variants of the Response Surface Method.

Nanoindentation, Third Edition gives a detailed account of the most up-to-date research in this important field of materials testing. As in previous editions, extensive theoretical treatments are provided and explained in a clear and consistent manner that will satisfy both experienced and novice scientists and engineers. Additionally, numerous examples of the applications of the technique are provided directly from manufacturers of nanoindentation instruments. A helpful series of appendices provides essential reference information that includes a list of frequently asked questions. The new edition has been restructured to provide results of the latest research and developments in the field of mechanical testing while retaining the essential background and introductory, but authoritative nature, of the previous editions. The new edition also expands on the instrumentation and applications chapters by including material sourced direct from the instrument manufacturers in this field. Aimed at graduate student level, this book is designed to fill a need associated with the use of nanoindentation as a quantitative test method for mechanical properties of small volumes of materials.

Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture.

This second volume of the series Lecture Notes in Applied and Computational Mechanics is the second part of the compendium of reviewed articles presented at the 11th EUROMECH-MECAMAT conference entitled "Mechanics of microstructured solids: cellular materials, fibre reinforced solids and soft tissues", which took place in Torino (Italy) in March 10-14, 2008, at the Museo Regional delle Scienze. This EUROMECH-MECAMAT conference was jointly organized by the Dipartimento di Matematica dell'Universita di Torino, Italy and the INPL Institute (LEMTA, Nancy-Universite, France). Prof. Franco Pastrone and Prof. Jean-Francois Ganghoffer were the co-chairmen.

Everything flows, so rheology is a universal science. Even if we set aside claims of such width, there can be no doubt of its importance in polymers. It joins with chemistry in the polymerisation step but polymer engineering is supreme in all the succeeding steps. This is the area concerned with the fabrication of the polymer into articles or components, with their design to meet the needs in service, and with the long and short term performance of the article or component. This is a typical area of professional engineering activity, but one as yet without its proper complement of professional engineers. An understanding of polymer rheology is the key to effective design and material plus process selection, to efficient fabrication, and to satisfactory service, yet few engineers make adequate use of what is known and understood in polymer rheology. Its importance in the flow processes of fabrication is obvious. Less obvious, but equally important, are the rheological phenomena which determine the in-service performance. There is a gap between the polymer rheologist and the polymer engineer which is damaging to both parties and which contributes to a less than satisfactory use of polymers in our society. It is important that this gap be filled and this book makes an attempt to do so. It presents an outline of what is known in a concise and logical fashion. It does this starting from first principles and with the minimum use of complex mathematics.

The editors have published a select group of full length papers on boundary element analysis (BEA) photographed from camera ready manuscripts. The articles have been prepared by some of the most distinguished and prolific individuals in this field. More than half of these articles have been submitted by authors that participated in an International Forum on Boundary Element Methods, in Melbourne Australia, in the Summer of 1991. However, this volume is not a conference proceedings, as these authors have expanded their accounts to chapter length, and/or have tailored their expositions more toward the style employed in archival journal publications. The authors that did not participate in the International Forum have also adhered to the above mentioned philosophy. This work contains a definitive representation of the significant capabilities and applications currently available or under investigation that fall under the general category of advanced boundary element analysis. With treatments of mechanical, thermal, fluid, and electromagnetic phenomena, this book should thus be of value to graduate students, practitioners, and researchers in engineering, mathematics, and the physical sciences wishing to obtain a broader perspective or remain current in these important areas of computational simulation.

The International Conference on Fracture Mechanics Technology Applied to Material Evaluation and Structure Design was held in Melbourne, Australia, from August 10 to 13, 1982. It was sponsored jointly by the Australian Fracture Group and Institute of Fracture and Solid Mechanics at Lehigh University. Pro fessor G. C. Sih of Lehigh University, Drs. N. E. Ryan and R. Jones of Aeronau tical Research Laboratories served as Co-Chairmen. They initiated the organiza tion of this international event to provide an opportunity for the practitioners, engineers and interested individuals to present and discuss recent advances in the evaluation of material and structure damage originating from defects or cracks. Particular emphases were placed on applying the fracture mechanics tech nology for assessing interactions between material properties, design and opera tional requirements. It is timely to hold such a Conference in Australia as she embarks on technology extensive industries where safeguarding structures from pre mature and unexpected failure is essential from both the technical and economical points. view The application of system-type approach to failure control owes much of its success to fracture mechanics. It is now generally accepted that the discipline, when properly implemented, provides a sound engineering basis for accounting in teractions between material properties, design, fabrication, inspection and op erational requirements. The approach offers effective solutions for design and maintenance of large-scale energy generation plants, mining machineries, oil ex ploration and retrieval equipments, land, sea and air transport vehicles."

Rapid Tooling Guidelines for Sand Casting describes the guidelines for the sand casting industry in using rapid tooling processes. Topics in the seven chapters include sand casting processes, tool design and construction, fast freeform fabrication processes, rapid tooling processes, sand casting dimension control, rapid tooling evaluation methods and decision making processes. Twelve case studies will also be examined in the book.

This volume constitutes the Proceedings of the IUTAM Symposium on 'Nonlinear Analysis of Fracture', held in Cambridge from 3rd to 7th Septem ber 1995. Its objective was to assess and place on record the current state of understanding of this important class of phenomena, from the standpoints of mathematics, materials science, physics and engineering. All fracture phenomena are nonlinear; the reason for inclusion of this qualification in the title was to reflect the intention that emphasis should be placed on distinctive aspects of nonlinearity, not only with regard to material consti tutive behaviour but also with regard to insights gained, particularly from the mathematics and physics communities, during the recent dramatic ad vances in understanding of nonlinear systems in general. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. The Symposium remained focussed on issues of practical significance for fracture phenomena, with concentration on aspects that are still im perfectly understood. The most significant unifying issue in this regard is that of scale: this theme was addressed from several perspectives. One important aspect is the problem of passing information on one scale up or down, as an input for analysis at another scale. Although this is not always the case, it may be that the microscopic process of fracture is understood in some particular class of materials."

Auf einer Sitzung des :Biiros der Internationalen Union fiir Theore- tische und Angewandte Mechanik (IUTAM) in :Briissel am 21. Septem- ber 1953 wurde beschlossen, ein Kolloquium iiber Festkorpermechanik (vorlaufiger Titel) fiir die letzte Septemberwoche 1955 zu pla.nen, und zwa.r in Madrid, entsprechend einer EinIadung, welche die Vertreter der zugehorigen spanischen Organisation Instituto Naciona.l de Tecnica Aeronautica "Esteban Terradas" (INTA) , die Herren A. NUNEz und A. PEREZ-MARiN personIich iiberbrachten. Das vom :Biiro der IUTAM hierfiir eingesetzte Wissenschaftliche Komitee bestand aus R. GRAMMEL als Vorsitzendem und den Herren TH. VON K.ARMiN, M. Roy und G. I. TAYLOR, das spanische Organisa- tions-Komitee aus den Herren A. NUNEz und A. PEREZ-MARiN samt einem Stab technischer und administrativer Mitarbeiter. In drei :Beratungen des Wissenschaftlichen Komitees (:Briissel, 27. Juli 1954; Farnborough, to. September 1954; Paris, 23. Mai 1955) wurde das Programm des Kolloquiums mit dem endgiiltigen Titel "Verformung und FlieBen des Festkorpers" festgelegt und dann in den Tagen vom 26. bis 30. September 1955 gemaB dem Plan von Seite IX verwirklicht. Jedes der drei Themen (Versetzungen und Plastizitat; Nichtlineare Elastizitat; Viskoelastizita.t und Relaxation) und insbesondere jede Sitzung wurde durch einen AIIgemeinen V ortrag eingeleitet. Die Titel aller V ortrage gibt das Inhaltsverzeichnis Seite XI und XII an. Die Vortrage wurden am 26., 27. und 29. September im Consejo Superior de Investigaciones Cientificas in Madrid gehalten, am 28. Sep- tember in Torrej6n de Ardoz, verbunden mit einer :Besichtigung der Laboratorien des INTA daselbst.

In keeping with the general trend towards rationalisation, static calculations have of late also been programmed by electronic computers. The number of problems which can be advan tageously resolved in this way is, however, very limited as yet, partly on account of the relati vely high cost involved and partly due to the waiting time the statician must suffer after collect ing together his data and, finally, because the programming possibilities of the computer are limited. Nonetheless, if static calculations have to be rationalised, there is another way: all beam structures-whether they be continuous beams or frame constructions-are arithmetically based on individual spans which are freely supported or fixed at the ends. If the basic values for these can be ascertained quickly and accurately, then a considerable part of the arithmetical work is already done. It is the aim of this work to provide the statician with these values. An attempt has been made to deal as comprehensively as possible with all the cases of loading likely to arise in practice. Naturally, one case or another is bound to happen more frequently whilst others are seldom encountered. However, this allembracing programme is intended to make it possible for the user of this work, after a brief, familiarising period, always to use the same arithmetical pro cedure, the choice of the actual method being left to him."

Most materials used in contemporary life and industry are heterogeneous (composites) and multicomponent, possessing a rich and complex internal structure. This internal structure, or microstructure, plays a key role in understanding and controlling the continuum behavior, or macroscopic, of a wide variety of materials. The modeling process is a critical tool for scientists and engineers studying the analysis and experimentation for the micromechanics and behavior of these materials. "Heterogeneous Media" is a critical, in-depth edited survey of the major topics surrounding the modeling and analysis of problems in micromechanics of multicomponent systems, including conceptual and practical aspects. The goal of this extensive and comprehensive survey is to provide both specialists and nonspecialists with an authoritative and interdisciplinary perspective of current ideas and methods used for modeling heterogeneous materials behavior and their applications. Topics and Features: * all chapters use interdisciplinary modeling perspective for investigating heterogeneous media*Five chapters provide self-contained discussions, with background provided*Focuses only upon most important techniques and models, fully exploring micro-macro interconnections*extensive introductory survey chapter on micromechanics of heterogeneous media*microstructure characterization via statistical correlation functions*micro-scale deformation of pore space*wave fields and effective dynamical properties*modeling of the complex production technologies for composite materials The book is ideal for a general scientific and engineering audience needing an in-depth view and guide to current ideas, methods and

The notion of continuum thermodynamics, adopted in this book, is primarily understood as a strategy for development of continuous models of various physical systems. The examples of such a strategy presented in the book have both the classical character (e. g. thermoelastic materials, viscous fluids, mixtures) and the extended one (ideal gases, Maxwellian fluids, thermoviscoelastic solids etc. ). The latter has been limited intentionally to non-relativistic models; many important relativistic applications of the true extended thermodynamics will not be considered but can be found in the other sources. The notion of extended thermodynamics is also adopted in a less strict sense than suggested by the founders. For instance, in some cases we allow the constitutive dependence not only on the fields themselves but also on some derivatives. In this way, the new thermodynamical models may have some features of the usual nonequilibrium models and some of those of the extended models. This deviation from the strategy of extended thermodynamics is motivated by practical aspects; frequently the technical considerations of extended thermodynamics are so involved that one can no longer see important physical properties of the systems. This book has a different form from that usually found in books on continuum mechanics and continuum thermodynamics. The presentation of the formal structure of continuum thermodynamics is not always as rigorous as a mathematician might anticipate and the choice of physical subjects is too disperse to make a physicist happy.