This volume constitutes the Proceedings of the IUTAM Symposium on "Analytical and Computational Fracture Mechanics of Non-homogeneous Materials," held in Cardiff from 18th to 22nd June 2001. The Symposium was convened to address and place on record topical issues in analytical and computational aspects of the fracture of non-homogeneous materials as they are approached by specialists in mechanics, materials science and related fields. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. Given the extensive range and scale of non-homogeneous materials, it had to be focussed to enhance the quality and impact of the Symposium. The range of non-homogeneous materials was limited to those that are inhomogeneous at the macroscopic level and/or exhibit strain softening. The issues of micro to macro scaling were not excluded even within this restricted range which covered materials such as rock, concrete, ceramics and composites on the one hand, and, on the other, those metallic materials whose ductile fracture is strongly influenced by the presence of inhomogeneities. The Symposium remained focussed on fundamental research issues of practical significance. These issues have many common features among seemingly disparate non-homogeneous materials.

A comprehensive treatment of "linear systems analysis" applied to dynamic systems as an approach to interdisciplinary system design beyond the related area of electrical engineering. The text gives an interpretation of mechanical vibrations based on the theory of dynamic systems, aiming to bridge the gap between existing theoretical methods in different engineering disciplines and to enable advanced students or professionals to model dynamic and vibrating systems with reference to communication and control processes. Emphasizing the theory it presents a balanced coverage of analytical principles and applications to vibrations with regard to mechatronic problems.

Structural Synthesis in Precision Elasticity reflects the summary of theoretical and experimental studies whose conclusions are effective for optimized structural synthesis in precision elasticity, as well as demonstrate a large experience and options in the synthesis, production, application of precision elastic guides, mechanisms, correctors, transducers, instruments and machines. The main focus of this book is in the possible simplification of the corresponding analytical apparatus by using kinematical equivalents, matrix methods, appropriate contours, and function expansion with enough accurate minimal polynomials. This approach allows for substitution of some known unwieldy formulae and methods that are not convenient for digestible and tractable synthesis.

The book consists of two main parts:

- The elastic systems functional analysis and structural synthesis methods, including effective approximations and references to the history of their development

- The application and development of precision functional elastic systems at reference and operating conditions, including the observation of archives with effective synthesized structures and elements of nanotechnology.

Each part provides theoretical basics and a large variety of examples and recommendations. This book gives theoretical and practical tools to researchers, precision machines, instruments and miniature systems designers, engineers, metrologists, and engineering students.

Despite that this book is dedicated to the general problems of the structural synthesis in precision elasticity, most of the practical examples and applications are concerned with the measuring systems as the precision is their main goal.

The author intends to show close connection between the elastic precision structures developed during the 20th century and even before and the new elastic systems for atomic force microscopy and other recently created advanced structures in precision elasticity.

The main advantages of sandwiches as structural components are now well known and well-established. Due to the progress in polymer science and engineering and advances in manufacturing processes, sandwich structures can blend various functional and structural properties and therefore lead to highly innovating systems. The current difficulty to overcome is to provide designers with proper methodologies and tools that could enable them to design improved sandwich structures. Such dedicated design tools should be efficient, reliable, flexible and user-friendly. They should be based on advanced knowledge of sandwich behaviour at global and local scales. Such approach relies on our capability to test, identify, control and model structure performances. The impressive variety of core and face materials and the rapid developments in forming processes give new opportunities to design components which have more complex shapes and higher integrated functional and structural properties. Interest in sandwiches is permanently growing in industry and refined testing and modelling approaches should be encouraged to set up relevant guidelines to design reliable advanced structures. The European Society for Mechanics sponsored the EUROMECH 360 Colloquium on the 'Mechanics of Sandwich Structures' in Saint-Etienne, France, on 13 - 15 May 1997. The main purpose of EUROMECH 360 was to go into the most recent progresses in sandwich analysis and design, including mechanical modelling and testing. It was expected that the Colloquium should contribute to define new research directions to support development of advanced applications in strategic industrial sectors such as ground transportations or building and civil engineering."

This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc .."

The area of material damage models has undergone a rapid development in the past few years. This is an extensive and comprehensive survey of one- and three-dimensional damage models for elastic and inelastic solids. The state-of-the-art is reported by about 200 references. The book not only provides a rich current source of knowledge, but also describes examples of practical applications, numerical procedures, and computer codes. The style of presentation is systematic, clear, and concise and is supported by illustrative diagrams.

In this book a new phenomenological approach to brittle medium fracture initiation under shock pulses is developped. It provides an opportunity to estimate fracture of media with and without macrodefects. A qualitative explanation is thus obtained for a number of principally important effects of high-speed dynamic fracture that cannot be clarified within the framework of previous approaches. It is possible to apply this new strategy to resolve applied problems of disintegration, erosion, and dynamic strength determination of structural materials. Specialists can use the methods described to determine critical characteristics of dynamic strength and optimal effective fracture conditions for rigid bodies. This book can also be used as a special educational course on deformation of materials and constructions, and fracture mechanics.

This book on mechanical microsensors is based on a course organized by the Swiss Foundation for Research in Microtechnology (FSRM) in Neuchatel, Swit zerland, and developed and taught by the authors. Support by FSRM is herewith gratefully acknowledged. This book attempts to serve two purposes. First it gives an overview on me chanical microsensors (sensors for pressure, force, acceleration, angular rate and fluid flow, realized by silicon micromachining). Second, it serves as a textbook for engineers to give them a comprehensive introduction on the basic design issues of these sensors. Engineers active in sensor design are usually educated either in electrical engineering or mechanical engineering. These classical educa tional pro grams do not prepare the engineer for the challenging task of sensor design since sensors are instruments typically bridging the disciplines: one needs a rather deep understanding of both mechanics and electronics. Accordingly, the book contains discussion of the basic engineering sciences relevant to mechanical sensors, hopefully in a way that it is accessible for all colours of engineers. Engi rd th neering students in their 3 or 4 year should have enough knowledge to be able to follow the arguments presented in this book. In this sense, this book should be useful as textbook for students in courses on mechanical microsensors (as is CUf rently being done at the University ofTwente)."

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.

This book offers comprehensive coverage of topics used in engineering solutions for the stiffness and strength of physical systems, with a range of scales from micrometers to kilometers. Coverage integrates a wide array of topics into a unified text, including such subjects as plasticity, fracture, composite materials, energy approaches, and mechanics of microdevices (MEMs). This integrated and unified approach reflects the reality of modern technology with its demands to learn the fundamentals of new subjects quickly.

This Volume contains the Proceedings of a French - Australian workshop held in Melbourne, Australia from 3-6 December 2001. Entitled "Coupling of Fluids, Structures and Waves in Aeronautics (CFSWA)", the workshop was principally organised by CSIRO Mathematical and Information Sciences, Dassault Aviation and CNRS. The main purpose was to explore new computational methods and tools for efficient multi-disciplinary design in aero- nautics. This enterprise strongly depends on modelling of coupled disciplines and development of associated multi-disciplinary simulation tools. As an example of the requirements, the original logo for the workshop illustrated coupled aeroelas- ticity, scattered radar waves and high lift problems. Optimisation is required with respect to mUltiple objectives under conflict. Among the many challenges to be addressed are mathematical, numerical and en- gineering problems involving coupled flows, structures and waves. Future prog- ress on these topics strongly depends on the physical and mathematical modelling of coupled disciplines and the development of associated multi-disciplinary simu- lation tools. Strong couplings require appropriate exchanges of different kinds of information: physical and geometrical description of models, coupling of Partial Differential Equations (PDEs) at interfaces, and specification of boundary condi- tions or multi-objective functions in optimisation or control problems. Validation of multi-physics software also requires ever more efficient and accurate graphic visualisation tools representing experimental and computational data stored in da- tabases.

This book was developed while I was teaching graduate courses on analysis, design and optimization of structures, in the United States, Europe and Israel. Structural analysis is a main part of any design problem, and the analysis often must be repeated many times during the design process. Much work has been done on design-oriented analysis of structures recently and many studies have been published. The purpose of the book is to collect together selected topics of this literature and to present them in a unified approach. It meets the need for a general text covering the basic concepts and methods as well as recent developments in this area. This should prove useful to students, researchers, consultants and practicing engineers involved in analysis and design of structures. Previous books on structural analysis do not cover most of the material presented in the book. The book deals with the problem of multiple repeated analyses (reanalysis) of structures that is common to numerous analysis and design tasks. Reanalysis is needed in many areas such as structural optimization, analysis of damaged structures, nonlinear analysis, probabilistic analysis, controlled structures, smart structures and adaptive structures. It is related to a wide range of applications in such fields as Aerospace Engineering, Civil Engineering, Mechanical Engineering and Naval Architecture.

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.

The present volume offers a state-of-the-art report on the various recent sci entific developments in the Theory of Porous Media (TPM) comprehending the basic theoretical concepts in continuum mechanics on porous and mul tiphasic materials as well as the wide range of experimental and numerical applications. Following this, the volume does not only address the sophisti cated reader but also the interested beginner in the area of Porous Media by presenting a collection of articles. These articles written by experts in the field concern the fundamental approaches to multiphasic and porous materials as well as various applications to engineering problems. In many branches of engineering just as in applied natural sciences like bio- and chemomechanics, one often has to deal with continuum mechanical problems which cannot be uniquely classified within the well-known disci plines of either "solid mechanics" or "fluid mechanics." These problems, characterized by the fact that they require a unified treatment of volumetri cally coupled solid-fluid aggregates; basically fall into the categories of either mixtures or porous media. Following this, there is a broad variety of problems ranging in this category as for example the investigation of reacting fluid mix tures or solid-fluid suspensions as well as the investigation of the coupled solid deformation and pore-fluid flow behaviour of liquid- and gas-saturated porous solid skeleton materials like geomaterials (soil, rock, concrete, etc. ), polymeric and metallic foams or biomaterials (hard and soft tissues, etc)."

Shock-induced dynamic fracture of solids is of practical importance in many areas of materials science, chemical physics, engineering, and geophysics. This book, by an international roster of authors, comprises a systematic account of the current state of research in the field, integrating the large amount of work done in the former Soviet Union with the work done in the West.
Topics covered include: Wave propagation, experimental techniques and measurements, spallation of materials of different classes (metals, ceramics, glasses, polymers), constitutive models of fracture processes, and computer simulations.

This volume records the Symposium on 'Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics', held at the University of Nottingham from 30th August to 3rd September 1994, sponsored by the International Union of Theoretical and Applied Mechanics and held in conjunction with the In- ternational Society for the Interaction of Mechanics and Mathematics. The advent of composite materials, together with their widespread use in recent years, has provided a powerful stimulus for advances in several somewhat ne- glected areas of solid mechanics. Exploitation of fibre-reinforced solids and laminates has rekindled interest in the theory and application of anisotropic elasticity and motivated study of many aspects of material inhomogeneity. The need to understand fibre-matrix interactions, especially in modelling metal- matrix composites and the forming of thermoplastic components has fostered advances in plasticity and viscoelasticity theory, to describe phenomena such as deformation-induced inhomogeneity and anisotropy. Plasticity and flow of granular media are also intrinsically nonlinear, giving rise, for example, to highly anisotropic and strongly localized effects, such as shear bands. Most materials contain impurities. These inclusions, even if microscopically isotropic, cause macroscopic anisotropy in an 'effective-medium' theory. Dy- namic behaviour is even more complex, since wave propagation reveals both attenuation and dispersion effects. Increased interest in finer-scaled compos- ites (nanotechnology and superlattices) and ultra-high frequency techniques continue to reveal new effects, due to inhomogeneity and microstructure. An example included here is lattice-induced dispersion for certain surface waves of relatively long wavelength.

Contributed by world-renowned specialists on the occasion of Paul Germain's 80th birthday, this unique book reflects the foundational works and the intellectual influence of this author. It presents the realm of modern thermomechanics with its extraordinary wealth of applications to the behaviour of materials, whether solid or fluid. The thirty-one contributions follow an easygoing autobiographical sketch by Paul Germain, and highlight the power and richness of a methodological approach to the phenomenology of many materials. This approach combines harmoniously thermodynamics and continuum theory in order to provide exploitable, thermodynamically admissible models of a large variety of behaviours and phenomena, including those of diffusion, thermoelasticity, viscoplasticity, relaxation, hysteresis, wetting, shape-memory effects, growth, phase transitions, stability, fracture, shocks, machining of materials, microstructured solids, complex fluids, etc. Especially aimed at graduate students, researchers, and engineers in mechanical engineering and materials science, this book also presents the state of the art in an active field of research and opens new horizons in other scientific fields, such as applied mathematics and applied physics, because of the intellectual satisfaction and remarkable efficiency provided by the advocated approach.

Presenting the most important results, methods, and open questions, this book describes and compares advanced models in fracture mechanics. The author introduces the required mathematical technique, mainly the theory of analytical functions, from scratch.

This book on the state of the art in "Multifield Problems" consists of selected articles based on a conference on this topic at the University of Stuttgart in 1999. The first two articles are contributions to the general modelling of multifield problems. S.S. Antman presents the important role of viscoelastic dissipation in the mathematical modelling of bifurcation analysis of nonlinear elasticity for large deformations. G.A. Maugin presents the basic theoretical foundations for the combination of three scales - the microscopic lattice of crystals, the mesoscopic thermomechanical model and the macroscopic con tinuum mechanics model for describing the propagation of phase transition fronts in terms of the Landau-Ginzburg theory and the modelling of nonlinear waves. The other contributions are associated with five main areas of multifield modelling such as two and multiphase flows, the mechanics of materials in terms of multiscaling, the interaction of solids and fluids, efficient solution methods of the discrete equations including adaptivity, and the modelling of contact and fracture."

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).

This volume contains the proceedings of the CEASlDragNet European Drag Reduction Conference held on 19-21 June 2000 in Potsdam, Germany. This conference, succeeding the First and Second European Forum on Laminar Flow Technology 1992 and 1996 respectively, was initiated by the European Drag Reduction Network (DragNet) and organised by DGLR (Deutsche Gesellschaft fUr Luft- und Raumfahrt - Lilienthal Oberth e. V. ) under the auspices ofCEAS (Confederation of European Aerospace Societies). The development of aerodynamic drag reduction technologies is driven by predictions of remarkable fuel savings, promising substantial improvements not only of aircraft efficiency but also of environmental compatibility. However, considerable efforts on an European scale are needed in order to develop, qualifY and demonstrate the means for their practical realisation. The primary aim of this conference was to provide a comprehensive survey of the current status of research, development and application in all disciplines of aerodynamic drag re- duction including laminar flow technology, adaptive wing concepts, turbulence and se- paration control, induced drag reduction and supersonic flow aspects. Besides aerodynamic topics the Call for Papers addressed also interdisciplinary aspects of design & system inte- gration, structures, materials, manufacturing, operations and maintenance. The Programme Committee (PC), responsible for the scientific preparation of the conference, consisted of CEAS representatives and DragNet board members (see following page).

The analysis and simulation of multifield problems have recently become one of the most actual and vivid areas of research. Although the individual subproblems of complex technical and physical phenomena often are understood separately, their interaction and coupling create not only new difficulties but also a complete new level and quality of interacting coupled field problems. Presented by leading experts this book includes recent results in these fields from the International Conference on Multifield Problems, April 8-10, 2002 at the University of Stuttgart, Germany.

Especially designed as self-sustaining oscillating systems, resonant robotic systems use the natural modes of oscillation of electromechanical modules for their movements. In fact, manipulator systems built on these principles demonstrate record-breaking characteristics in performance. The authors summarize the results and experience of research on, and development of, resonant robotic systems. For the readers convenience, a presentation of design concepts is followed by solutions to new dynamical and control problems. The book is intended for designers, researchers and graduate students.

Experiments with rubber balloons and rubber sheets have led to surprising observations, some of them hitherto unknown or not previously described in the literature. In balloons, these phenomena are due to the non-monotonic pressure-radius characteristic which makes balloons a subject of interest to physicists engaged in stability studies. Here is a situation in which symmetry breaking and hysteresis may be studied analytically, because the stress-stretch relations of rubber - and its non-convex free energy - can be determined explicitly from the kinetic theory of rubber and from non-linear elasticity. Since rubber elasticity and the elasticity of gases are both entropy-induced, a rubber balloon represents a compromise between the entropic tendency of a gas to expand and the entropic tendency of rubber to contract. Thus rubber and rubber balloons furnish instructive paradigms of thermodynamics. This monograph treats the subject at a level appropriate for post-graduate studies.

A knowledge of the mechanical behaviour of both naturally occurring materials, such as soils and rocks, and artificial materials such as concrete and industrial granular matter, is of fundamental importance to their proper use in engineering and scientific applications. This volume contains selected lectures by international experts on current developments and problems in the numerical modelling of cohesive-frictional materials which provide a deeper understanding of the microscopic and macroscopic description of such materials. This book fills a gap by emphasizing the cross-fertilization of ideas between engineers and scientists engaged in this exciting field of research.