Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended.

The key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin films, smart materials, and structural and topology optimization. One lecture deals with a topic important for nanomaterials: the passage from discrete to continuum problems by using nonlinear homogenization methods. Some papers reveal the role of parameterized or Young measures in description of microstructures and in optimal design. Other papers deal with recently developed methods both analytical and computational for estimating the effective behavior and field fluctuations in composites and polycrystals with nonlinear constitutive behavior.

All in all, the volume offers a cross-section of current activity in nonlinear homogenization including a broad range of physical and engineering applications. The careful reader will be able to identify challenging open problems in this still evolving field. For instance, there is the need to improve bounding techniques for nonconvex problems, as well as for solving geometrically nonlinear optimum shape-design problems, using relaxation and homogenization methods."

This book offers a state-of-the-art overview and includes recent developments of various direct computational analysis methods. It is based on recently developed and widely employed numerical procedures for limit and shakedown analysis of structures and their extensions to a wide range of physical problems relevant to the design of materials and structural components. The book can be used as a complementary text for advanced academic courses on computational mechanics, structural mechanics, soil mechanics and computational plasticity and it can be used a research text.

This book presents a liber amicorum dedicated to Wolfgang H. Muller, and highlights recent advances in Prof. Muller's major fields of research: continuum mechanics, generalized mechanics, thermodynamics, mechanochemistry, and geomechanics. Over 50 of Prof. Muller's friends and colleagues contributed to this book, which commemorates his 60th birthday and was published in recognition of his outstanding contributions.

This is the first book devoted to a systematic description of the linear theory of piezoelectric shells and plates theory. The book contains two parts. In the first part, the theories for electroelastic thin-walled elements of arbitrary form with different directions of preliminary polarization are presented in an easy form for practical use. The approximate methods for integrating the equations of piezoelectric shells and plates are developed and applied for solving some engineering problems. In the second part, the theory of piezoelectric shells and plates is substantiated by the asymptotic method. The area of applicability for different kinds of electroelastic shell theories is studied. A new problem concerning the electroelastic phenomena at the edge of a thin-walled element is raised and solved.
The Theory of Piezoelectric Shells and Plates will be valuable to researchers working in the field of electroelasticity as well as to electrical and electronic engineers who use thin-walled piezoelements. It is also be helpful for students and post-graduates specializing in mechanics and for scientists concerning asymptotic methods.

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.

Self contained, this book presents a thorough introduction to the complementary notions of physical forces and material (or configurational) forces. All the required elements of continuum mechanics, deformation theory and differential geometry are also covered. This book will be a great help to many, whilst revealing to others a rather new facet of continuum mechanics in general, and elasticity in particular. An organized exposition of continuum mechanics on the material manifold is given which allows for the consideration of material inhomogeneities in their most appropriate framework. In such a frame the nonlinear elasticity of anisotropic inhomogenous materials appears to be a true field theory. Extensions to the cases of electroelasticity and magnetelasticity are then straightforward. In addition, this original approach provides systematic computational means for the evaluation of characteristic parameters which are useful in various branches of applied mechanics and mathematical physics. This is the case for path-independent integrals and energy-release rates in brittle fracture, the influence of electromagnetic fields on fracture criteria (such as in ceramics), the notion of momentum of electromagnetic fields in matter in optics, and the perturbation of solitons propagating in elastic dispersive systems.

Despite their apparent simplicity, the behaviour of pendulums can be remarkably complicated. Historically, pendulums for specific purposes have been developed using a combination of simplified theory and trial and error. There do not appear to be any introductory books on pendulums, written at an intermediate level, and covering a wide range of topics. This book aims to fill the gap. It is written for readers with some background in elementary geometry, algebra, trigonometry and calculus. Historical information, where available and useful for the understanding of various types of pendulum and their applications, is included. Perhaps the best known use of pendulums is as the basis of clocks in which a pendulum controls the rate at which the clock runs. Interest in theoretical and practical aspects of pendulums, as applied to clocks, goes back more than four centuries. The concept of simple pendulums, which are idealised versions of real pendulums is introduced. The application of pendulums to clocks is described, with detailed discussion of the effect of inevitable differences between real pendulums and simple pendulums. In a clock, the objective is to ensure that the pendulum controls the timekeeping. However, pendulums are sometimes driven, and how this affects their behaviour is described. Pendulums are sometimes used for occult purposes. It is possible to explain some apparently occult results by using modern pendulum theory. For example, why a ring suspended inside a wine glass, by a thread from a finger, eventually strikes the glass. Pendulums have a wide range of uses in scientific instruments, engineering, and entertainment. Some examples are given as case studies. Indexed in the Book Citation Index- Science (BKCI-S)

This book contains contributions from leading researchers in biomechanics, nanomechanics, tribology, contact mechanics, materials science and applications on various experimental techniques including atomic force microscopy (AFM) for studying soft, biomimetic and biological materials and objects. Biologists, physicists, researchers applying methods of contact mechanics and researchers testing materials using indentation techniques along with many other applied scientists will find this book a useful addition to their libraries. Moreover, several reviews in this book are written as introductions to several important and rather sophisticated research areas such as depth-sensing indentation, studying of biological cells by AFM probes, mechanics of adhesive contact and contact between viscoelastic (hereditary elastic) solids. The book containing new theoretical models, results of experimental studies and numerical simulations, along with reviews of above mentioned areas of contact mechanics in application to biological systems, would be beneficial for researchers in many areas of biology, medicine, engineering, mechanics and biomimetics.

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.

This volume details the principles underlying rapid solidification processing, material structure and properties, and their applications. This practical resource presents a manifold approach to both amorphous and crystalline rapidly solidified metallic alloys.;Written by over 30 internationally acclaimed specialists in their respective fields, Rapidly Solidified Alloys: surveys nucleation and growth studies in undercooled melts; examines various processes for the production of rapidly solidified alloys; discusses the compaction of amorphous alloys; describes surface remelting treatments for the rapid solidification of surface layers and the resultant improved workpiece properties; covers the closely related topics of structural relaxation, atomic transport and other thermally induced processes; demonstrates microstructure-property relationships in rapidly quenched crystalline alloy systems and their beneficial effects in applications; and elucidates the basic, engineeering, and applications-oriented magnetic properties of amorphous alloys.;Furnishing more than 2300 literature citations for further study of specific subjects, Rapidly Solidified Alloys is intended for materials, mechanical, product, and civil engineers; metallurgists; magneticians; physicists; physical chemists; and graduate students in these disciplines.

This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined.

This open access book presents established methods of structural health monitoring (SHM) and discusses their technological merit in the current aerospace environment. While the aerospace industry aims for weight reduction to improve fuel efficiency, reduce environmental impact, and to decrease maintenance time and operating costs, aircraft structures are often designed and built heavier than required in order to accommodate unpredictable failure. A way to overcome this approach is the use of SHM systems to detect the presence of defects. This book covers all major contemporary aerospace-relevant SHM methods, from the basics of each method to the various defect types that SHM is required to detect to discussion of signal processing developments alongside considerations of aerospace safety requirements. It will be of interest to professionals in industry and academic researchers alike, as well as engineering students. This article/publication is based upon work from COST Action CA18203 (ODIN - http://odin-cost.com/), supported by COST (European Cooperation in Science and Technology). COST (European Cooperation in Science and Technology) is a funding agency for research and innovation networks. Our Actions help connect research initiatives across Europe and enable scientists to grow their ideas by sharing them with their peers. This boosts their research, career and innovation.

New developments in the response spectrum method have led to calculations in seismic stresses that are more accurate, and usually lower, than those obtained by conventional methods. This new textbook examines the wealth of information on the response spectrum method generated by the latest research and presents the background theory in simplified form.
Applications of these methods is essential in the seismic design of critical structures, such as nuclear power plants and petroleum facilities. In new construction, the reduced seismic stresses will result in efficient and economic design. For facilities already built, these more accurate methods can be used where the facility is being reassessed for higher loads and in the calculation of margins.
Written by an acknowledged expert in this and related fields, this volume is ideal as a graduate text for courses in structural and earthquake engineering. It is also an excellent reference for civil, structural, mechanical, and earthquake engineers.

This book presents various questions of continuum mechanical modeling in the context of experimental and numerical methods, in particular, multi-field problems that go beyond the standard models of continuum mechanics. In addition, it discusses dynamic problems and practical solutions in the field of numerical methods. It focuses on continuum mechanics, which is often overlooked in the traditional division of mechanics into statics, strength of materials and kinetics. The book is dedicated to Prof. Volker Ulbricht, who passed away on April 9, 2021.

This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail.

This book addresses the hydrostatics and stability of ships and other floating marine structures - a fundamental aspect of naval architecture and offshore engineering for naval architects and marine engineers. It starts from the most basic concepts, assuming that the reader has no prior knowledge of the subject. By presenting the topic in a methodical and step-by-step manner, the book helps students to enhance their understanding, while also providing valuable guidelines for lecturers teaching related courses.

This edited volume summarizes research being pursued within the DFG Priority Programme 1748: "Reliable Simulation Methods in Solid Mechanics. Development of non-standard discretisation methods, mechanical and mathematical analysis", the aim of which was to develop novel discretisation methods based e.g. on mixed finite element methods, isogeometric approaches as well as discontinuous Galerkin formulations, including a sound mathematical analysis for geometrically as well as physically nonlinear problems. The Priority Programme has established an international framework for mechanical and applied mathematical research to pursue open challenges on an inter-disciplinary level. The compiled results can be understood as state of the art in the research field and show promising ways of further research in the respective areas. The book is intended for doctoral and post-doctoral students in civil engineering, mechanical engineering, applied mathematics and physics, as well as industrial researchers interested in the field.

About the book: This book is the first comprehensive review on acoustic metamaterials; novel materials which can manipulate sound waves in surprising ways, which include collimation, focusing, cloaking, sonic screening and extraordinary transmission. It covers both experimental and theoretical aspects of acoustic and elastic waves propagating in structured composites, with a focus on effective properties associated with negative refraction, lensing and cloaking. Most related books in the field address electromagnetic metamaterials and focus on numerical methods, and little (or no) experimental section. Each chapter will be authored by an acknowledged expert, amongst the topics covered will be experimental results on non-destructive imaging, cloaking by surface water waves, flexural waves in thin plates. Applications in medical ultrasound imaging and modeling of metamaterials will be emphasized too. The book can serve as a reference for researchers who wish to build a solid foundation of wave propagation in this class of novel materials.

Thin shells are three-dimensional structures with a dimension (the thickness) small with respect to the two others.Such thin structures are widely used in automobileandaviation industries,or in civil engineering, because they provide animportantsti?ness, due to theircurvature,with a small weight. Fig. 0.1. Airbus A380 Fig. 0.2. Hemispherical roof (Marseille, France) One ofthechallenges is often to reduce the weight (andconsequently the thickness)oftheshells, preservingtheirsti?ness.So that it is essential to have 1 accuratemodelsforthinandevenverythinshells ,andtobeabletocomputethe displacements resultingfromagivenloading.In particular, singularities leading to fractures in some cases must be absolutely predicted a priori and ofcourse avoided (see Fig.0.3 forexample). Since the pioneeringmodels of Novozhilov-Donnell [81] and Koiter [65][66], numerous works havebeen devoted to establish linear and non linear elastic shell model usingdirect orsurfacic approaches [18][25][100]. More recently, the asymptoticmethods [87] havebeen used, to try tojustify rigorously, fromthe three-dimensional equations, the shell models obtained by direct approaches - lying onapriori assumption, andto construct new models [54][55]. This way, 1 Very thin shells are present in certain domains of industry, as plastic ?lms for pa- aging or for electronics, streched sails, or even very thin metal sheets obtained by drawing. E. Sanchez-Palencia et al.: Singular Problems in Shell Theory, LNACM 54, pp. 1-11.

model. They conclude that the models using three fitting parameters provide the best fit over a wide range of suctions. Models for soil-water characteristic curves are only useful if we have experimental data on which to base them. Agus, Leong and Rahardjo (Singapore) present a large number of experimental soil-water characteristic curves determined for two types of residual soil from Sigapore. They present data for eight different sites. This data set allows them to relate the parameters of the soil-water characteristic curves to index properties. They conclude that the relationships derived are suitable to pro vide a quick preliminary estimate of a soil-water characteristic curve. The importance of soil-water characteristic curves is emphasized by another con tribution dealing with this topic. Aung, Rahardjo, Leong and Toll (Singapore) inves tigate the relationship between mercury intrusion porosimetry measurements and soil-water characteristic curves. The porosimetry measurements are presented as soil-air characteristic curves. The slopes of the soil-air characteristic curves are found to be similar to the slopes of the soil-water characteristic curves. The equiv alent pore diameters calculated from the mercury entry value and the air entry value appear to be related. Therefore, it is suggested that porosimetry data can be used to construct an estimate of the soil-water characteristic curve."

This monograph details spatial and material vistas on non-linear continuum mechanics in a dissipation-consistent approach. Thereby, the spatial vista renders the common approach to nonlinear continuum mechanics and corresponding spatial forces, whereas the material vista elaborates on configurational mechanics and corresponding material or rather configurational forces. Fundamental to configurational mechanics is the concept of force. In analytical mechanics, force is a derived object that is power conjugate to changes of generalised coordinates. For a continuum body, these are typically the spatial positions of its continuum points. However, if in agreement with the second law, continuum points, e.g. on the boundary, may also change their material positions. Configurational forces are then power conjugate to these configurational changes. A paradigm is a crack tip, i.e. a singular part of the boundary changing its position during crack propagation, with the related configurational force, typically the J-integral, driving its evolution, thereby consuming power, typically expressed as the energy release rate. Taken together, configurational mechanics is an unconventional branch of continuum physics rationalising and unifying the tendency of a continuum body to change its material configuration. It is thus the ideal formulation to tackle sophisticated problems in continuum defect mechanics. Configurational mechanics is entirely free of restrictions regarding geometrical and constitutive nonlinearities and offers an accompanying versatile computational approach to continuum defect mechanics. In this monograph, I present a detailed summary account of my approach towards configurational mechanics, thereby fostering my view that configurational forces are indeed dissipation-consistent to configurational changes.

This book presents a novel continuum finite deformation framework addressing the complex interactions among electrostatics, species transport, and mechanics in solid networks immersed in a fluid phase of solvent and ions. Grounded on cutting-edge multiphysics theories for soft active materials, the proposed model is primarily applied to ionic polymer metal composites (IPMCs). First, the influence of shear deformation on the IPMC response is analyzed through semi-analytical solutions obtained via the method of matched asymptotic expansions. Second, the novel electrochemo-poromechanical theory is used to predict the curvature relaxation and electric discharge that are observed in IPMC actuation and sensing, respectively, under a sustained stimulus. This newly formulated theory is, in turn, applied to biological cell clusters. Here, important mechanical considerations are integrated into classical bioelectrical models, thus offering novel insights into the interplay of mechanical and electrical signaling in the coordination of developmental processes.

This book presents interdisciplinary, cutting-edge and creative applications of graph theory and modeling in science, technology, architecture and art. Topics are divided into three parts: the first one examines mechanical problems related to gears, planetary gears and engineering installations; the second one explores graph-based methods applied to medical analyses as well as biological and chemical modeling; and the third part includes various topics e.g. drama analysis, aiding of design activities and network visualisation. The authors represent several countries in Europe and America, and their contributions show how different, useful and fruitful the utilization of graphs in modelling of engineering systems can be. The book has been designed to serve readers interested in the subject of graph modelling and those with expertise in related areas, as well as members of the worldwide community of graph modelers.

This book contains technical papers, presented at the International Workshop on Connections and the Behaviour, Strength and Design of Steel Structures, on topics including local analysis of joints, modeling of load-deflection behaviour, methods of frame analysis, and design requirements and codes.

This book comprises select papers from the International Conference on Emerging Trends in Civil Engineering (ICETCE 2018). Latest research findings in different branches of civil engineering such as structural engineering, construction materials, geotechnical engineering, water resources engineering, environmental engineering, and transportation infrastructure are covered in this book. The book also gives an overview of emerging topics like smart materials and structures, green building technologies, and intelligent transportation system. The contents of this book will be beneficial for students, academicians, industrialists and researchers working in the field of civil engineering.