The approach to plasticity theory developed here is firmly rooted in thermodynamics. Emphasis is placed on the use of potentials and the derivation of incremental response, necessary for numerical analysis. The derivation of constitutive models for irreversible behaviour entirely from two scalar potentials is shown.

The use of potentials allows models to be very simply defined, classified and, if necessary, developed and it permits dependent and independent variables to be interchanged, making possible different forms of a model for different applications.

The theory is extended to include treatment of rate-dependent materials and a powerful concept, in which a single plastic strain is replaced by a plastic strain function, allowing smooth transitions between elastic and plastic behaviour is introduced.

This monograph will benefit academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers; it will also interest numerical analysts in engineering mechanics.

Friction contacts are used to transmit forces or to dissipate energy. The aim of this second edition is to describe an efficient procedure to model dynamical contact problems with friction. This procedure is applied to different practical problems and validated by experiments. A thorough understanding of friction phenomena can lead to improvements like the reduction of noise and maintenance costs, increased useful life of machines and improved energy efficiency.

This self-tutorial offers a concise yet thorough grounding in the mathematics necessary for successfully applying FEMs to practical problems in science and engineering. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite-element methods instead of passively absorbing the material, as in most standard textbooks. The enlarged English-language edition, based on the original French, also contains a chapter on the approximation steps derived from the description of nature with differential equations and then applied to the specific model to be used. Furthermore, an introduction to tensor calculus using distribution theory offers further insight for readers with different mathematical backgrounds.

Mechanochemistry as a branch of solid state chemistry enquires into processes which proceed in solids due to the application of mechanical energy. This provides a thorough, up to date overview of mechanochemistry of solids and minerals. Applications of mechanochemistry in nanoscience with special impact on nanogeoscience are described. Selected advanced identification methods, most frequently applied in nanoscience, are described as well as the advantage of mechanochemical approach in minerals engineering. Examples of industrial applications are given. Mechanochemical technology is being applied in many industrial fields: powder metallurgy (synthesis of nanometals, alloys and nanocompounds), building industry (activation of cements), chemical industry (solid waste treatment, catalyst synthesis, coal ashes utilization), minerals engineering (ore enrichment, enhancement of processes of extractive metallurgy), agriculture industry (solubility increase of fertilizers), and pharmaceutical industry (improvement of solubility and bioavailability of drugs).

This reference serves as an introduction to newcomers to mechanochemistry, and encourages more experienced researchers to broaden their knowledge and discover novel applications in the field.

This book is an introduction to level set methods and dynamic implicit surfaces. These are powerful techniques for analyzing and computing moving fronts in a variety of different settings. While it gives many examples of the utility of the methods to a diverse set of applications, it also gives complete numerical analysis and recipes, which will enable users to quickly apply the techniques to real problems. The book begins with a description of implicit surfaces and their basic properties, then devises the level set geometry and calculus toolbox, including the construction of signed distance functions. Part II adds dynamics to this static calculus. Topics include the level set equation itself, Hamilton-Jacobi equations, motion of a surface normal to itself, re-initialization to a signed distance function, extrapolation in the normal direction, the particle level set method and the motion of co-dimension two (and higher) objects. Part III is concerned with topics taken from the fields of Image Processing and Computer Vision. These include the restoration of images degraded by noise and blur, image segmentation with active contours (snakes), and reconstruction of surfaces from unorganized data points. Part IV is dedicated to Computational Physics. It begins with one phase compressible fluid dynamics, then two-phase compressible flow involving possibly different equations of state, detonation and deflagration waves, and solid/fluid structure interaction. Next it discusses incompressible fluid dynamics, including a computer graphics simulation of smoke, free surface flows, including a computer graphics simulation of water, and fully two-phase incompressible flow. Additional related topics include incompressible flames with applications to computer graphics and coupling a compressible and incompressible fluid. Finally, heat flow and Stefan problems are discussed. A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.

17 2 STRESS FIELDS FOR SIMPLE STRUCTURES 2. 1 INTRODUCTION In this chapter the behavior and strength of simple structures made of rein forced or prestressed concrete is investigated with the aid of stress fields. In particular, the webs and flanges of beams, simple walls, brackets, bracing beams and joints of frames are investigated. By this means, the majority of design cases are already covered. In reality, all structural components are three-dimensional. Here, however, components are considered either directly as two-dimensional plate elements (i. e. the plane stress condition with no variation of stress over the thickness of the element) or they are subdivided into several plates. Since two-dimensional structural elements are statically redundant, it is pOSSible for a particular loading to be in equilibrium with many (theoretically an infinite number of) stress states. If the lower bound method of the theory of plasticity is employed, then an admissible stress field or any combination of such stress fields may be selected. In chapter 4 it is shown that this method is suitable for the design of reinforced concrete structures, and the consequence of the choice of the final structural system on the structural behavior is dealt with in detail. The first cases of the use of this method date back to Ritter [6] and Morsch [4], who already at the beginning of the century investigated the resultants of the internal stresses by means of truss models.

In this second edition a new chapter has been added covering the buffeting theory in a finite element format. The motivation for this has been that a finite element format is becoming more and more dominant in all areas of structural mechanics. It is streamlined for computer programming, and it facilitates the use of general purpose routines that are applicable in several types of structural engineering problems. In this book the finite element formulation of the problem of dynamic response calculations follows the general principle of virtual work, a general principle which may be found in many other text books. While the buffeting wind load itself has with no trouble been included in a finite element format, the main challenge has been to obtain a consistent formulation that includes all the relevant motion induced forces. This has been important, because, while many structures (e.g. long-span suspension bridges) may suffer greatly and become unstable at high wind velocities, the same structures may also benefit from these effects at the design wind velocity. It is well known that motion induced forces will change the stiffness and damping properties of the combined structure and flow system. If calculations are performed for a suitably close set of increasing mean wind velocities and the changing mechanical properties (stiffness and damping) are updated from one velocity to the next, then the response of the system may be followed up to wind velocities close to the stability limit, i.e. up to response values that are perceived as unduly large. Finite element calculations may be performed in time domain, in frequency domain or converted into a modal format. All these options have been included. Pursuing a time domain solution strategy requires the use of the so-called indicial functions. The theory behind such a formulation is also covered, and the determination of these functions from aerodynamic derivatives has been included in a separate appendix.

This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.

Since January 1990, when the first edition ofthis first-of-a-kind book appeared, there has been much experimental and theoretical progress in the multi disciplinary subject of tribology and mechanics of magnetic storage devices. The subject has matured into a rigorous discipline, and many university tribology and mechanics courses now routinely contain material on magnetic storage devices. The major growth in the subject has been on the micro- and nanoscale aspects of tribology and mechanics. Today, most large magnetic storage industries use atomic force microscopes to image the magnetic storage components. Many companies use variations of AFMs such as friction force microscopes (FFMs) for frictional studies. These instruments have also been used for studying scratch, wear, and indentation. These studies are valuable in the fundamental understanding of interfacial phenomena. In the second edition, I have added a new chapter, Chapter 11, on micro and nanoscale aspects of tribology and mechanics of magnetic storage compo nents. This chapter presents the state of the art of the micro/nanotribology and micro/nanomechanics of magnetic storage components. In addition, typographical errors in Chapters 1 to 10 and the appendixes have been corrected. These additions update this book and make it more valuable to researchers of the subject. I am grateful to many colleagues and particularly to my students, whose work is reported in Chapter 11. I thank my wife, Sudha, who has been forbearing during the progress of the research reported in this chapter.

Lamb waves are guided waves that propagate in thin plate or shell structures. There has been a clear increase of interest in using Lamb waves for identifying structural damage, entailing intensive research and development in this field over the past two decades. Now on the verge of maturity for diverse engineering applications, this emerging technique serves as an encouraging candidate for facilitating continuous and automated surveillance of the integrity of engineering structures in a cost-effective manner. In comparison with conventional nondestructive evaluation techniques such as ultrasonic scanning and radiography which have been well developed over half a century, damage identification using Lamb waves is in a stage of burgeoning development, presenting a number of technical challenges in application that need to be addressed and circumvented. It is these two aspects that have encouraged us to write this book, with the intention of consolidating the knowledge and know-how in the field of Lamb-wave-based damage identification, and of promoting widespread attention to mature application of this technique in the practical engineering sphere. This book provides a comprehensive description of key facets of damage identification technique using Lamb waves, based on the authors' knowledge, comprehension and experience, ranging from fundamental theory through case studies to engineering applications.

This monograph deals with the behavior of essentially nonlinear heterogeneous materials in processes occurring under intense dynamic loading, where microstructural effects play the main role. This book is not an introduction to the dynamic behavior of materials, and general information available in other books is not included. The material herein is presented in a form I hope will make it useful not only for researchers working in related areas, but also for graduate students. I used it successfully to teach a course on the dynamic behavior of materials at the University of California, San Diego. Another course well suited to the topic may be nonlinear wave dynamics in solids, especially the part on strongly nonlinear waves. About 100 problems presented in the book at the end of each chapter will help the reader to develop a deeper understanding of the subject. I tried to follow a few rules in writing this book: (1) To focus on strongly nonlinear phenomena where there is no small parameter with respect to the amplitude of disturbance, including solitons, shock waves, and localized shear. (2) To take into account phenomena sensitive to materials structure, where typical space scale of material parameters (particle size, cell size) are presented in the models or are variable in experimental research.

sections dealing with fuzzy functions and fuzzy random functions are certain to be of special interest. The reader is expected to be in command of the knowledge gained in a basic university mathematics course, with the inclusion of stochastic elements. A specification of uncertainty in any particular case is often difficult. For this reason Chaps. 3 and 4 are devoted solely to this problem. The derivation of fuzzy variables for representing informal and lexical uncertainty reflects the subjective assessment of objective conditions in the form of a membership function. Techniques for modeling fuzzy random variables are presented for data that simultaneously exhibit stochastic and nonstochastic properties. The application of fuzzy randomness is demonstrated in three fields of civil engineering and computational mechanics: structural analysis, safety assessment, and design. The methods of fuzzy structural analysis and fuzzy probabilistic structural analysis developed in Chap. 5 are applicable without restriction to arbitrary geometrically and physically nonlinear problems. The most important forms of the latter are the Fuzzy Finite Element Method (FFEM) and the Fuzzy Stochastic Finite Element Method (FSFEM).

Solid cellular materials (foams, lattice materials, honeycombs, etc.) are attractive and have resulted in the creation of an active subject for structural, mechanical and material scientists in recent years. Indeed, constant progress in the manufacturing techniques are improving their properties and reducing their costs; and mass productions and industrial applications are beginning. An important mechanical problem is how to characterize and model the mechanical behaviour of these materials, which is necessary for industrial design and numerical predictions involved in various applications such as light weight structures, energy absorbers. This volume contains twenty-two contributions written by distinguished invited speakers from all part of the world to the iutam symposium on mechanical properties of cellular materials. It provides a survey on recent advances in the characterisation and modeling of the mechanical properties of solid cellular materials under static and dynamic loading as well as their applications in lightweight structures analysis and design. This volume will be of interest to structural, mechanical and material scientists and engineers working on different aspects of this new class of materials (for example in microstructure observation, micromechanical and multiscale modeling, phenomenological models, structural impact behaviour and numerical validation).

This textbook on models and modeling in mechanics introduces a new unifying approach to applied mechanics: through the concept of the open scheme, a step-by-step approach to modeling evolves. The unifying approach enables a very large scope on relatively few pages: the book treats theories of mass points and rigid bodies, continuum models of solids and fluids, as well as traditional engineering mechanics of beams, cables, pipe flow and wave propagation.

This book presents new ideas in the framework of novel, finite element discretization schemes for solids and structure, focusing on the mechanical as well as the mathematical background. It also explores the implementation and automation aspects of these technologies. Furthermore, the authors highlight recent developments in mixed finite element formulations in solid mechanics as well as novel techniques for flexible structures at finite deformations. The book also describes automation processes and the application of automatic differentiation technique, including characteristic problems, automatic code generation and code optimization. The combination of these approaches leads to highly efficient numerical codes, which are fundamental for reliable simulations of complicated engineering problems. These techniques are used in a wide range of applications from elasticity, viscoelasticity, plasticity, and viscoplasticity in classical engineering disciplines, such as civil and mechanical engineering, as well as in modern branches like biomechanics and multiphysics.

Observations of uncertainty in measured data with time improves forecasting capability in a wide range of fields in engineering. This book provides an introduction to uncertainty forecasting based on fuzzy time series. It details descriptive, modeling, and forecasting methods for fuzzy time series. Coverage places emphasis on forecasting based on fuzzy random processes as well as forecasting involving fuzzy neuronal networks.

In this book, a new approach is pioneered in providing a unified theory in continuum mechanics. General Continuum Mechanics is intended for the beginner, but it develops advanced material covering interdisciplinary subjects. With applications of convective, Lagrangian, and Eulerian coordinates and the first and second laws of thermodynamics, the first-year graduate student will learn solid mechanics and fluid mechanics as an integrated subject. Electromagnetic continuum and relativistic continuum are included. The conservational properties of mass, momentum, and energy on earth and in the universe constitute the ingredients of this book. They are the monumental contributions of Newton, Maxwell, and Einstein, a panorama of beauty of universal laws that evolved over the last four centuries. No boundaries are needed to separate them, but rather we integrate them in harmony and place them in perspective. This is the book for interdisciplinary studies to carry out the modern scientific projects in which engineering, physics, and applied mathematics must be combined.

Models should be as simple as possible, but no simpler. For the physics of polymeric liquids, whose relevant lengths and time scales are out of reach for first principles calculations, this means that we have to choose a minimum set of sufficiently detailed descriptors such as architecture (linear, ring, branched), connectivity, semiflexibility, stretchability, excluded volume, and hydrodynamic interaction. These 'universal' fluids allow the prediction of material properties under external flow- or electrodynamic fields, the results being expressed in terms of reference units, specific for any particular chosen material. This book provides an introduction to the kinetic theory and computer simulation methods needed to handle these models and to interpret the results. Also included are a number of sample applications and computer codes.

Mechanical engineering, and engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a series featuring graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of c- centrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of series editors, each an expert in one of the areas of concentration. The names of the series editors are listed on page vi of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. Preface This book is based on my experience with the control systems of antennas and radiotelescopes. Overwhelmingly, it is based on experience with the NASA Deep Space Network (DSN) antennas. It includes modeling the antennas, developing control algorithms, eld testing, system identi cation, performance evaluation, and 1 troubleshooting. My previous book emphasized the theoretical aspects of antenna control engineering, while this one describes the application part of the antenna control engineering.

A real boon for those studying fluid mechanics at all levels, this work is intended to serve as a comprehensive textbook for scientists and engineers as well as advanced students in thermo-fluid courses. It provides an intensive monograph essential for understanding dynamics of ideal fluid, Newtonian fluid, non-Newtonian fluid and magnetic fluid. These distinct, yet intertwined subjects are addressed in an integrated manner, with numerous exercises and problems throughout.

Everyone involved with the mechanics of composite materials and structures must have come across the works of Dr. N.J. Pagano in their research. His research papers are among the most referenced of all existing literature in the field of mechanics of composite materials. This monograph makes available, in one volume, all Dr. Pagano's major technical papers. Most of the papers included in this volume have been published in the open literature, but there are a few exceptions -- a few key, unpublished reports have been included for continuity. The topics are: some basic studies of anisotropic behavior, exact solutions for elastic response, role of micromechanics, and some carbon--carbon spinoffs. The volume can be used as a reference book by researchers in academia, industry, and government laboratories, and it can be used as a reference text for a graduate course on the mechanics of composite materials.

This book is the ?rst of severalSolids volumes in theShock Wave Science and Technology Reference Library. These volumes are primarily concerned with high-pressure shock waves in solid media, including detonation, high-velocity impact, and penetration. Thisvolumecontainseightarticles.The?rstthreedescriberecent, exciting advancesinthreeexperimentalareas: ultrashortshockdynamicsattheatomic and molecular scale, very-high pressure equations of state measurements using the Z accelerator, and failure waves associated with impact failure of brittle solids. The subsequent four chapters are foundational, covering eq- tionsofstate, elastic plasticshockwaves, continuumplasticity, andnumerical methods. The ?nal article describes recent progress in mesoscale modeling of heterogeneous reactive solids. The articles are each self-contained, and can be read independently of each other, though, of course, they are thematically interrelated. They o?er a timely reference, for beginners as well as professional scientists and engineers, coveringboththefoundationsandnewviewpointsofshockwavesinsolids, and includeburgeoningdevelopments.Thefollowingaresupplementarycomments on some of the outstanding issues described in this volume. For many decades the primary signi?cance of shock wave research in solids has been the determination of high-pressure equations of state (EOS) for weapons analysis, geophysics and astrophysics applications, as well as mat- ials science focusing on the synthesis of ultra-hard materials such as diamo

In this edited book various novel approaches to problems of current interest in civil engineering are demonstrated. The topics range from dynamic band seismic problems to the analysis of long-span structures and ancient buildings. Experts associated within the Lagrange Laboratory present recent research results on functionally-graded or composite materials, granular materials, geotechnics, as well as frictional or adhesive contact problems.

From July 10th through July 13th, 1994, an informal workshop co-organized by RILEM committees 116-PCD and 123-MME was held at Saint-Remy-Ies Chevreuse, France, and attended by 38 delegates from 16 countries. Twenty-nine papers were presented, converging the general subjects of modelling micro structures and predicting durability of concrete and other cement-based materials. A short summary follows: G. M. Idom's paper entitled "Modelling Research for Concrete Engineering" serves as an introduction to the workshop, presenting an overview of modelling research with the conelusion that the broad practica1 objective is to produce high-quality concrete. This means that many characteristics, ranging from rheology to alkali-silica reaction, must be modelled. In other words, the system must be understood. Idom's paper sets the stage for papers in two general areas: 1) models and 2) transport properties. After this, abrief survey of the develop ment of microstructurally-based models is presented. A elose relationship between computer power and speed is suggested. The first group of papers on models covers the subjects of scale and resolution. Most models define and predict characteristics of the pore system, which range in scale from nanometer to millimeter. Various types ofnetworks are proposed in these papers. A good microstructural model must describe the pores and other phases at ascale appropriate to the properties that the model predicts. Also, a good model should be based on fundamental knowledge. In the case of cement-based materials, the important properties may depend on the microstructure, especially the porosity, at several scales."

The mechanics of structures with initial stresses is a traditional part of structural mechanics. It is closely related to the important problem of stability of structures. The basic concepts of elastic stability of structures go back to works by Euler (1759) and Bryan (1889). Later, it was found that the problem of deformation of solids with initial stresses is related to variational principles and nonlinear problems in elasticity; see Trefftz (1933), Marguerre (1938), Prager (1947), Hill (1958), Washuzu (1982). Historical detail up to the 1940s can be found in the book by Timoshenko (1953). Observing the basic concepts of the traditional mechanics of stressed structures, we agree that these are suitable for uniform structural elements (plates, beams, and so on) made of homogeneous materials, but not for complex structures (such as a network plate or a lattice mast) or structures made of composite materials (such as fiber reinforced or textile materials). Many concepts of the classical theory, such as a cross section or neutral plane (axis), correspond to no mechanical objects if we consider an inhomogeneous structure. As a result, we come to the conclusion that it would be useful to have a theory of thin inhomogeneous structures developed on the basis of 3-D elasticity theory with no simplifying assumptions (with no a priori hypothesis).