The aim of the book is the presentation of the fundamental mathematical and physical concepts of continuum mechanics of solids in a unified description so as to bring young researchers rapidly close to their research area. Accordingly, emphasis is given to concepts of permanent interest, and details of minor importance are omitted. The formulation is achieved systematically in absolute tensor notation, which is almost exclusively used in modern literature. This mathematical tool is presented such that study of the book is possible without permanent reference to other works.

Rigorous presentation of Mathematical Homogenization Theory is the subject of numerous publications. This book, however, is intended to fill the gap in the analytical and numerical performance of the corresponding asymptotic analysis of the static and dynamic behaviors of heterogenous systems. Numerous concrete applications to composite media, heterogeneous plates and shells are considered. A lot of details, numerical results for cell problem solutions, calculations of high-order terms of asymptotic expansions, boundary layer analysis etc., are included.

Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems.
The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials.

Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of "handouts" to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation.

Superplasticity is the ability of polycrystalline materials under certain conditions to exhibit extreme tensile elongation in a nearly homogeneous/isotropic manner. Historically, this phenomenon was discovered and systematically studied by metallurgists and physicists. They, along with practising engineers, used materials in the superplastic state for materials forming applications. Metallurgists concluded that they had the necessary information on superplasticity and so theoretical studies focussed mostly on understanding the physical and metallurgi cal properties of superplastic materials. Practical applications, in contrast, were led by empirical approaches, rules of thumb and creative design. It has become clear that mathematical models of superplastic deformation as well as analyses for metal working processes that exploit the superplastic state are not adequate. A systematic approach based on the methods of mechanics of solids is likely to prove useful in improving the situation. The present book aims at the following. 1. Outline briefly the techniques of mechanics of solids, particularly as it applies to strain rate sensitive materials. 2. Assess the present level of investigations on the mechanical behaviour of superplastics. 3. Formulate the main issues and challenges in mechanics ofsuperplasticity. 4. Analyse the mathematical models/constitutive equations for superplastic flow from the viewpoint of mechanics. 5. Review the models of superplastic metal working processes. 6. Indicate with examples new results that may be obtained using the methods of mechanics of solids."

Non Destructive Testing and Non Destructive Evaluation using Ultrasounds covers an important field of applications and requires a wide range of fundamental theoretical, numerical and experimental investigations. In the present volume, the reader will find some relevant research results on wave propagation in complex materials and structures which are concerned with today 's problems on composites, bonding, guided waves, contact or damage, imaging and structural noise. The fifth meeting of the Anglo-French Research Group on "Wave propagation in non homogeneous media with a view to Non Destructive testing" was held in Anglet, France, June 2-6, 2008.

Adaptronic structures and systems are engineered to adjust automatically to variable operating and environmental conditions, through the use of feedback control. The authors of this book have taken on the task of comprehensively describing the current state of the art in this highly modern and broadly interdisciplinary field. The book presents selected examples of applications, and goes on to demonstrate current development trends.

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.

This book contains the most relevant papers presented in the International Conference on Materials Forming, ESAFORM 2005. It gathers selected plenary and keynote papers presented in the conference, offering an up-to-date synthesis of the academic and industrial research in the fields of physical and numerical modeling of materials forming processes.

This is the second, enhanced and updated edition of an essential text for students of mechatronics. It covers both the detailed physical modeling of mechatronic systems and their precise numerical simulation using the Finite Element (FE) method. New material includes a section discussing locking effects as occurring in the numerical computation of thin mechanical structures as well as a new chapter on computational aeroacoustics to study the complex phenomenon of flow induced noise.

In the paper the author attempts to assess the fatigue life of chosen welded joints. It focuses especially on chosen problems that accompany deter- nation of the fatigue life of welded joints, taking into consideration the strain energy density parameter. Chapter 2 describes the welded joint as a stress concentrator. The state of stress and strain in the notch are described and theoretical and fatigue coefficients are indicated. The fatigue coef- cient of the notch effect is estimated on the basis of fictitious radius in the notch root. Chapter 3 presents a model of fatigue life assessment under uniaxial stress state with statistical handling of data presented. The new energy model of fatigue life assessment, which rests upon the analysis of stress and strain in the critical plane, is described in detail in chapter 4. The principle of such a description is presented in the uniaxial as well as in - axial state of loading. Chapter 5 contains the analysis of tests of four ma- rials subjected to different loadings: cyclic, variable-amplitude with Ga- sian distribution, and variable amplitude with Gaussian distribution and overloading for symmetric and pulsating loading. The analysis is based on the determined fatigue characteristics for all the considered materials. Chapter 6 shows the application of the model in the fatigue life assessment in the complex state of loading (bending with torsion of flange-tube and tube-tube joints) based on fatigue research of steel and aluminum welded joints carried out in well-known German centres.

Themethodologyfordesigninghigh-performancecompositestructuresisstill evo- ing. The complexity of the response of composite materials and the dif?culties in predicting the composite material properties from the basic properties of the c- stituents result in the need for a well-planned and exhaustive test program. The recommended practice to mitigate the technological risks associated with advanced composite materials is to substantiate the performance and durability of the design in a sequence of steps known as the Building Block Approach. The Building Block Approach ensures that cost and performance objectives are met by testing greater numbers of smaller, less expensive specimens. In this way, technology risks are assessed early in the program. In addition, the knowledge acquired at a given level of structural complexity is built up before progressing to a level of increased complexity. Achieving substantiation of structural performance by testing alone can be p- hibitively expensive because of the number of specimens and components required to characterize all material systems, loading scenarios and boundary conditions. Building Block Approachprogramscan achieve signi?cant cost reductionsby se- ing a synergy between testing and analysis. The more the development relies on analysis, the less expensive it becomes. The use of advanced computational models for the prediction of the mechanical response of composite structures can replace some of the mechanical tests and can signi?cantly reduce the cost of designing with composites while providing to the engineers the information necessary to achieve an optimized design.

The researchers in Aerodynamics know that there is not a unitary method of investigation in this field. The first mathematical model of the air plane wing, the model meaning the integral equation governing the phe nomenon, was proposed by L. Prandtl in 1918. The integral equation deduced by Prandtl, on the basis of some assumptions which will be specified in the sequeL furnishes the circulation C(y) (see Chapter 6). U sing the circulation, one calculates the lift and moment coefficients, which are very important in Aerodynamics. The first hypothesis made by Prandtl consists in replacing the wing by a distribution of vortices on the plan-form D of the wing (i. e. the projection of the wing on the plane determined by the direction of the uniform stream at infinity and t he direction of the span of the wing). Since such a distribution leads to a potential flow in the exterior of D and the experiences show that downstream the flow has not this character, Prandtl introduces as a sup plementary hypothesis another vortices distribution on the trace of the domain D in the uniform stream. The first kind of vortices are called tied vortices and the second kind of vortices are called free vortices."

Multibody Mechanics and Visualization is designed to appeal to computer-savvy students who will acquire significant skills in mathematical and physical modelling of mechanical systems in the process of producing attractive computer simulations and animations. The emphasis here is on general skills with all-round applicability rather than the ability to solve "cooked-up problems. The approachable style and clear presentation of this text will help you grasp the essentials of: modeling the kinematics and dynamics of arbitrary multibody mechanisms; formulating a mathematical description of general motions of such mechanisms; implementing the description in a computer-graphics application for the animation/visualization of the movement. Multibody Mechanics and Visualization plays down the prediction of dynamics by formal analysis of differential equations while preparing its students to perform such analyses with greater understanding later. The text relies on the following principles for effective tuition: an inductive approach to learning - discerning general patterns from particular observations; repetition and review of important principles to reinforce your learning through numerous examples; obvious visual guidance that shows you at a glance which information you need for different levels of understanding; computer tools, visual representations and elements of active learning integrated into the text to suit the way you want to learn. Supported in the text in parallel with the theoretical presentation is the simulation and animation application Mambo. In contrast with existing commercially available educational software tools, Mambo requires detailed input from you in order to define the specific geometry of a mechanism as well as the differential equations governing its behavior while allowing you to visualize the results of your efforts. The Mambo toolbox enables you to provide these specifications for mechanisms that would pose insurmountable algebraic challenges to manual calculation. With these tools, you will be able to see the implications of decisions made throughout the modeling process, to check your mathematical analyses, and to enjoy the fruit of your labor Mambo can be freely downloaded from the author's website and runs under any version of MS Windows(r). The toolbox is compatible with the Maple software environment and the Matlab(r) extended symbolic toolbox."

Computer simulations not only belong to the most important methods for the theoretical investigation of granular materials, but provide the tools that have enabled much of the expanding research by physicists and engineers. The present book is intended to serve as an introduction to the application of numerical methods to systems of granular particles. Accordingly emphasis is on a general understanding of the subject rather than on the presentation of latest advances in numerical algorithms. Although a basic knowledge of C++ is needed for the understanding of the numerical methods and algorithms in the book, it avoids usage of elegant but complicated algorithms to remain accessible for those who prefer to use a different programming language. While the book focuses more on models than on the physics of granular material, many applications to real systems are presented.

This volume contains the proceedings of the IUTAM Symposium on Ela- ohydrodynamics and Microelastohydrodynamics held in Cardiff from 1st to 3rd September 2004. The symposium focused on theoretical, experimental and computational issues in elastohydrodynamic lubrication (EHL) both in relation to smooth surfaces and in situations where the ?lm is of the same order or th- ner than the surface roughness (micro-EHL). The last IUTAM Symposium in this general area of contact of deformable bodies was in 1974. The emphasis in the Symposium was upon fundamental issues such as: solution methods; lubricant rheological models, thermal effects; both low and high elastic m- ulus situations; human and replacement joints; ?uid traction; dynamic effects, asperity lubrication and the failure of lubrication; surface fatigue and thermal distress under EHL conditions. Delegates were welcomed to Wales and the Cardiff School of Engine- ing by the head of the School, Professor Hywel Thomas. The opening l- ture was given jointly by Professor Duncan Dowson, FRS and Sir Gordon Higginson, the distinguished partnership which produced some of the most important numerical solutions to the fundamental EHL problem which led to the ?rst reliable ?lm thickness formula for isothermal, Newtonian conditions. Their presentation reviewed the early developments in the subject and included some fascinating details of the dif?culties overcome and the scienti?c pers- alities involved. A total of 33 presentations were given over a period of three days.

Proceedings of the IUTAM Symposium on Fluid- Structure Interaction in Ocean Engineering, held in Hamburg, July 23-26, 2007. The study of gravity driven water waves interacting with fixed or freely floating objects is an active and important field of research in ocean engineering. The accurate prediction of large amplitude ship motions or of marine structures in severe seas is still a delicate problem in the field of fluid-structure interaction. While three-dimensional panel methods have reached the state of maturity in linear sea-keeping analysis, the original problem, governed by strongly nonlinear boundary conditions, is far from being solved efficiently. The principal nonlinearities are associated with the variable wetted surface of the ship hull or the floating body and with the nonlinear hydrodynamic conditions on the free surface. Moreover, marine structures often must be modelled as multibody systems rather than a single body. This causes additional problems due to wave slamming on floating and fixed structures. Furthermore, problems such as coupled structural behavior of submerged or floating systems as well as various wind effects have to be considered for the proper design of offshore systems. This book collects contributions from leading scientists working on the following topics: Ocean waves, probabilistic models of sea waves, fluid-loading on structures including pipes, cables, drill-strings etc., behavior of floating systems, stability and capsizing of ships, coupled structural behavior, sloshing in tanks, CFD validation and verification.

This book guides the reader through general and fundamental problems of pressure vessel design. The basic approach is rigorously scientific with a complete theoretical development of the topics treated. The concrete and precise calculation criteria provided can be immediately applied to actual designs. The book also comprises unique contributions on important topics like Deformed Cylinders, Flat Heads, or Flanges.

Machining is one of the most important manufacturing processes. Parts manufactured by other processes often require further operations before the product is ready for application. "Machining: Fundamentals and Recent Advances" is divided into two parts. Part I explains the fundamentals of machining, with special emphasis on three important aspects: mechanics of machining, tools, and work-piece integrity. Part II is dedicated to recent advances in machining, including: machining of hard materials, machining of metal matrix composites, drilling polymeric matrix composites, ecological machining (minimal quantity of lubrication), high-speed machining (sculptured surfaces), grinding technology and new grinding wheels, micro- and nano-machining, non-traditional machining processes, and intelligent machining (computational methods and optimization). Advanced students, researchers and professionals interested or involved in modern manufacturing engineering will find the book a useful reference.

This is an up-to-date review of developments in the field of bifurcations and instabilities in geomechanics from some of the world 's leading experts. Leading international researchers and practitioners of the topics debate the developments and applications which have occurred over the last few decades. Beside fundamental research findings, applications in geotechnical, petroleum, mining, and bulk materials engineering are emphasised.

This book addresses the characterization of flow and transport in porous fractured media from experimental and modeling perspectives. It provides a comprehensive presentation of investigations performed and analyzed on different scales.

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.

Materials engineers, researchers and students will find this book a valuable resource on erosion wear mechanisms. It contains extensive data on erosive wear resistance of conventional steels, powder materials and coatings, and criteria for erosive wear-resistant material and coating selection. The book collects together the work of more than 130 industrially-supported research projects conducted over 50 years.

In the past ?ve decades considerable attention has been devoted to comp- ite materials. A number of expressions have been suggested by which mac- scopic properties can be predicted when the properties, geometry, and volume concentrations of the constituent components are known. Many expressions are purely empirical or semi-theoretical. Others, however, are theoretically well founded such as the exact results from the following classical boundary studies: Bounds for the elastic moduli of composites made of perfectly coherent homogeneous, isotropic linear elastic phases have been developed by Paul [1] and Hansen [2] for unrestricted phase geometry and by Hashin and Shtrikman [3] for phase geometries, which cause macroscopic homogeneity and isotropy. The composites dealt with in this book are of the latter type. For two speci?c situations (later referred to), Hashin [4] and Hill [5] derived exact - lutionsforthebulkmodulusofsuchmaterials.Hashinconsideredtheso-called Composite Spheres Assemblage (CSA) consisting of tightly packed congruent composite elements made of spherical particles embedded in concentric - trix shells. Hill considered materials in which both phases have identical shear moduli. In the ?eld of predicting the elastic moduli of homogeneous isotropic c- posite materials in general the exact Hashin and Hill solutions are of th- retical interest mainly. Only a few real composites have the geometry de?ned by Hashin or the sti?ness distribution assumed by Hill. The enormous sign- icance, however, of the Hashin/Hill solutions is that they represent bounds which must not be violated by sti?ness predicted by any new theory claiming to consider geometries in general.