As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine “Kyiv Polytechnic Institute�. The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine and the USA.

This volume presents a collection of contributions on materials modeling, which were written to celebrate the 65th birthday of Prof. Nobutada Ohno. The book follows Prof. Ohno’s scientific topics, starting with creep damage problems and ending with homogenization methods.

This volume contains the Proceedings of the 3rd IFToMM Symposium on Mechanism Design for Robotics, held in Aalborg, Denmark, 2-4 June, 2015. The book contains papers on recent advances in the design of mechanisms and their robotic applications. It treats the following topics: mechanism design, mechanics of robots, parallel manipulators, actuators and their control, linkage and industrial manipulators, innovative mechanisms/robots and their applications, among others. The book can be used by researchers and engineers in the relevant areas of mechanisms, machines and robotics.

This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers and Chapter 9, which addresses various perturbational aspects in contact problems and introduces the sensitivity of articular contact mechanics. This book is intended for advanced undergraduate and graduate students, researchers in the area of biomechanics, and engineers interested and involved in the analysis and design of thin-layer structures.

This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment of Analytical Mechanics.

This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

This textbook offers an introduction to modeling the mechanical behavior of solids within continuum mechanics and thermodynamics. To illustrate the fundamental principles, the book starts with an overview of the most important models in one dimension. Tensor calculus, which is called for in three-dimensional modeling, is concisely presented in the second part of the book. Once the reader is equipped with these essential mathematical tools, the third part of the book develops the foundations of continuum mechanics right from the beginning. Lastly, the book's fourth part focuses on modeling the mechanics of materials and in particular elasticity, viscoelasticity and plasticity. Intended as an introductory textbook for students and for professionals interested in self-study, it also features numerous worked-out examples to aid in understanding.

The book presents interesting examples of recent developments in this area. Among the studied materials are bulk metallic glasses, metamaterials, special composites, piezoelectric smart structures, nonwovens, etc. The last decades have seen a large extension of types of materials employed in various applications. In many cases these materials demonstrate mechanical properties and performance that vary significantly from those of their traditional counterparts. Such uniqueness is sought – or even specially manufactured – to meet increased requirements on modern components and structures related to their specific use. As a result, mechanical behaviors of these materials under different loading and environmental conditions are outside the boundaries of traditional mechanics of materials, presupposing development of new characterization techniques, theoretical descriptions and numerical tools. The book presents interesting examples of recent developments in this area. Among the studied materials are bulk metallic glasses, metamaterials, special composites, piezoelectric smart structures, nonwovens, etc.

This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches�, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

This book presents and discusses mathematical models, numerical methods and computational techniques used for solving coupled problems in science and engineering. It takes a step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all of the complex couplings involved in the physical description. Simulation of multifaceted physics problems is a common task in applied research and industry. Often a suitable solver is built by connecting together several single-aspect solvers into a network. In this book, research in various fields was selected for consideration: adaptive methodology for multi-physics solvers, multi-physics phenomena and coupled-field solutions, leading to computationally intensive structural analysis. The strategies which are used to keep these problems computationally affordable are of special interest, and make this an essential book.

An original mechanical formulation to treat nonlinear orthotropic behavior of composite materials is presented in this book. It also examines different formulations that allow us to evaluate the behavior of composite materials through the composition of its components, obtaining a new composite material. Also two multiple scale homogenization methods are given, one based on the analytical study of the cells (Ad-hoc homogenization) and other one, more general based on the finite element procedure applied on the macro scale (upper-scale) and in the micro scale (sub-scale). A very general formulation to simulate the mechanical behavior for traditional composite structures (plywood, reinforced concrete, masonry, etc.), as well as the new composite materials reinforced with long and short fibers, nanotubes, etc., are also shown in this work. Typical phenomena occurring in composite materials are also described in this work, including fiber-matrix debonding, local buckling of fibers and its coupling with the overall buckling of the structure. Finally, several numerical examples that evaluates the qualities and capabilities of the general model formulated are offered in this book. This book is intended for graduate engineering students who want to expand their knowledge of composite structures behavior.

This book contains a collection of the state-of-the-art reviews written by the leading researchers in the areas of nanoscale mechanics, molecular dynamics, nanoscale modeling of nanocomposites and mechanics of carbon nanotubes. No other book provides reviews of recent discoveries such as a nanoscale analog of the Pauli’s principle, i.e., effect of the spatial exclusion of electrons or the SEE effect, a new Registry Matrix Analysis for the nanoscale interfacial sliding and new data on the effective viscosity of interfacial electrons in nanoscale stiction at the interfaces. This volume is also an exceptional resource on the well tested nanoscale modeling of carbon nanotubes and nanocomposites, new nanoscale effects, unique evaluations of the effective thickness of carbon nanotubes under different loads, new data on which size of carbon nanotubes is safer and many other topics. Extensive bibliography concerning all these topics is included along with the lucid short reviews. Numerous illustrations are provided for molecular dynamic simulations, fascinating nanoscale phenomena and remarkable new effects. It is of interest to a wide range of researchers and students.

This book presents the latest results related to shells characterize and design shells, plates, membranes and other thin-walled structures, a multidisciplinary approach from macro- to nanoscale is required which involves the classical disciplines of mechanical/civil/materials engineering (design, analysis, and properties) and physics/biology/medicine among others. The book contains contributions of a meeting of specialists (mechanical engineers, mathematicians, physicists and others) in such areas as classical and non-classical shell theories. New trends with respect to applications in mechanical, civil and aero-space engineering, as well as in new branches like medicine and biology are presented which demand improvements of the theoretical foundations of these theories and a deeper understanding of the material behavior used in such structures.

This book provides an insight into current research topics, focusing special attention exactly on welding issues. The presented research work demonstrates that application of synchrotron and neutron radiation in combination with other techniques enables the basic understanding of material-related processes to be extended appreciably. It also shows ways of how to improve new materials and their use in industry. Following on from the 1st workshop in 2009 at BAM Berlin, a 2nd workshop dealing with this subject matter was held in 28-30 November, 2012 in Osaka/Japan with international participation of scientists from sixteen countries. The book includes selected contributions from the various subject blocks, precisely covering issues of practical and immediately implementable benefit to industrial enterprises. Therefore, peer-reviewed papers dealing with the following topics are contained as well: - Phase transformation during welding, metallurgy and material development - Evolution and significance of residual stresses - Investigations into laser and electron beam welding

This book describes for the first time a simulation method for the fast calculation of contact properties and friction between rough surfaces in a complete form. In contrast to existing simulation methods, the method of dimensionality reduction (MDR) is based on the exact mapping of various types of three-dimensional contact problems onto contacts of one-dimensional foundations. Within the confines of MDR, not only are three dimensional systems reduced to one-dimensional, but also the resulting degrees of freedom are independent from another. Therefore, MDR results in an enormous reduction of the development time for the numerical implementation of contact problems as well as the direct computation time and can ultimately assume a similar role in tribology as FEM has in structure mechanics or CFD methods, in hydrodynamics. Furthermore, it substantially simplifies analytical calculation and presents a sort of "pocket book edition" of the entirety contact mechanics. Measurements of the rheology of bodies in contact as well as their surface topography and adhesive properties are the inputs of the calculations. In particular, it is possible to capture the entire dynamics of a system - beginning with the macroscopic, dynamic contact calculation all the way down to the influence of roughness - in a single numerical simulation model. Accordingly, MDR allows for the unification of the methods of solving contact problems on different scales. The goals of this book are on the one hand, to prove the applicability and reliability of the method and on the other hand, to explain its extremely simple application to those interested.

This book focuses on civil and structural engineering and construction management applications. The contributions constitute modified, extended and improved versions of research presented at the  minisymposium organized by the editors at the ECCOMAS conference on this topic in Barcelona 2014.

The book is focused on constitutive description of mechanical behaviour of engineering materials: both conventional (polycrystalline homogeneous isotropic or anisotropic metallic materials) and non-conventional (heterogeneous multicomponent anisotropic composite materials). Effective material properties at the macro-level depend on both the material microstructure (originally isotropic or anisotropic) as well as dissipative phenomena occurred on fabrication and consecutive loading phase (hardening) resulting in irreversible microstructure changes (acquired anisotropy). The material symmetry is a background and anisotropy is a core around which the book is formed. In this way a revision of classical rules of enhanced constitutive description of materials is required.

During the last years computational methods lead to new approaches that can be applied within medical practice. Based on the tremendous advances in medical imaging and high-performance computing, virtual testing is able to help in medical decision processes or implant designs. Current challenges in medicine and engineering are related to the application of computational methods to clinical medicine and the study of biological systems at different scales. Additionally manufacturers will be able to use computational tools and methods to predict the performance of their medical devices in virtual patients. The physical and animal testing procedures could be reduced by virtual prototyping of medical devices. Here simulations can enhance the performance of alternate device designs for a range of virtual patients. This will lead to a refinement of designs and to safer products. This book summarizes different aspects of approaches to enhance function, production, initialization and complications of different types of implants and related topics.

This book presents the latest findings on mechanical and materials engineering as applied to the design of modern engineering materials and components. The contributions cover the classical fields of mechanical, civil and materials engineering, as well as bioengineering and advanced materials processing and optimization. The materials and structures discussed can be categorized into modern steels, aluminium and titanium alloys, polymers/composite materials, biological and natural materials, material hybrids and modern nano-based materials. Analytical modelling, numerical simulation, state-of-the-art design tools and advanced experimental techniques are applied to characterize the materials’ performance and to design and optimize structures in different fields of engineering applications.

This book presents a systematic approach in performing reliability assessment of solder joints using Finite Element (FE) simulation. Essential requirements for FE modelling of an electronic package or a single reflowed solder joint subjected to reliability test conditions are elaborated. These cover assumptions considered for a simplified physical model, FE model geometry development, constitutive models for solder joints and aspects of FE model validation. Fundamentals of the mechanics of solder material are adequately reviewed in relation to FE formulations. Concept of damage is introduced along with deliberation of cohesive zone model and continuum damage model for simulation of solder/IMC interface and bulk solder joint failure, respectively. Applications of the deliberated methodology to selected problems in assessing reliability of solder joints are demonstrated. These industry-defined research-based problems include solder reflow cooling, temperature cycling and mechanical fatigue of a BGA package, JEDEC board-level drop test and mechanisms of solder joint fatigue. Emphasis is placed on accurate quantitative assessment of solder joint reliability through basic understanding of the mechanics of materials as interpreted from results of FE simulations. The FE simulation methodology is readily applicable to numerous other problems in mechanics of materials and structures.

The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement - longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement - cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement - Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics - from the students at an advanced undergraduate and graduate level to the scientists, professionally interesting in waves. But mechanics is understood in the broad sense, when it includes mechanical and other engineering, material science, applied mathematics and physics and so forth. The genesis of this book can be found in author's years of research and teaching while a head of department at SP Timoshenko Institute of Mechanics (National Academy of Sciences of Ukraine), a member of Center for Micro and Nanomechanics at Engineering School of University of Aberdeen (Scotland) and a professor at Physical-Mathematical Faculty of National Technical University of Ukraine "KPI". The book comprises 11 chapters. Each chapter is complemented by exercises, which can be used for the next development of the theory of nonlinear waves.

This book focuses on the way in which the problem of the motion of bodies has been viewed and approached over the course of human history. It is not another traditional history of mechanics but rather aims to enable the reader to fully understand the deeper ideas that inspired men, first in attempting to understand the mechanisms of motion and then in formulating theories with predictive as well as explanatory value. Given this objective, certain parts of the history of mechanics are neglected, such as fluid mechanics, statics and astronomy after Newton. On the other hand, due attention is paid, for example, to the history of thermodynamics, which has its own particular point of view on motion. Inspired in part by historical epistemology, the book examines the various views and theories of a given historical period (synchronic analysis) and then makes comparisons between different periods (diachronic analysis). In each period, one or two of the most meaningful contributions are selected for particular attention, instead of presenting a long inventory of scientific achievements.

This book discusses the mechanical properties of ceramics and aims to provide both a solid background for undergraduate students, as well as serving as a text to bring practicing engineers up to date with the latest developments in this topic so they can use and apply these to their actual engineering work. Generally, ceramics are made by moistening a mixture of clays, casting it into desired shapes and then firing it to a high temperature, a process known as 'vitrification'. The relatively late development of metallurgy was contingent on the availability of ceramics and the know-how to mold them into the appropriate forms. Because of the characteristics of ceramics, they offer great advantages over metals in specific applications in which hardness, wear resistance and chemical stability at high temperatures are essential. Clearly, modern ceramics manufacturing has come a long way from the early clay-processing fabrication method, and the last two decades have seen the development of sophisticated techniques to produce a large variety of ceramic material. The chapters of this volume are ordered to help students with their laboratory experiments and guide their observations in parallel with lectures based on the current text. Thus, the first chapter is devoted to mechanical testing. A chapter of ductile and superplastic ceramic is added to emphasize their role in modern ceramics (chapter 2). These are followed by the theoretical basis of the subject. Various aspects of the mechanical properties are discussed in the following chapters, among them, strengthening mechanisms, time dependent and cyclic deformation of ceramics. Many practical illustrations are provided representing various observations encountered in actual ceramic-structures of particularly technical significance. A comprehensive list of references at the end of each chapter is included in this textbook to provide a broad basis for further studying the subject. The work also contains a unique chapter on a topic not discussed in other textbooks on ceramics concerning nanosized ceramics. This work will also be useful as a reference for materials scientists, not only to those who specialize in ceramics.

The State-of-the-Art Report of RILEM Technical Committee 228-MPS on Mechanical properties of Self-Compacting Concrete (SCC) summarizes an extensive body of information related to mechanical properties and mechanical behaviour of SCC. Due attention is given to the fact that the composition of SCC varies significantly. A wide range of mechanical properties are considered, including compressive strength, stress-strain relationship, tensile and flexural strengths, modulus of elasticity, shear strength, effect of elevated temperature, such as fire spalling and residual properties after fire, in-situ properties, creep, shrinkage, bond properties and structural behaviour. A chapter on fibre-reinforced SCC is included, as well as a chapter on specialty SCC, such as light-weight SCC, heavy-weight SCC, preplaced aggregate SCC, special fibre reinforced SCC and underwater concrete.