Understanding the elastoplastic deformation of metals and geomaterials, including the constitutive description of the materials and analysis of structure undergoing plastic deformation, is an essential part of the background required by mechanical, civil, and geotechnical engineers as well as materials scientists. However, most books address the subject at a introductory level and within the infinitesimal strain context.

Elastoplasticity Theory takes a different approach in an advanced treatment presented entirely within the framework of finite deformation. This comprehensive, self-contained text includes an introduction to nonlinear continuum mechanics and nonlinear elasticity. In addition to in-depth analysis of the mathematical and physical theories of plasticity, it furnishes an up-to-date look at contemporary topics, such as plastic stability and localization, monocrystalline plasticity, micro-to-macro transition, and polycrysalline plasticity models.

Elastoplasticity Theory reflects recent trends and advances made in the theory of plasticity over the last four decades. It will not only help stimulate further research in the field, but will enable its readers to confidently select the appropriate constitutive models for the materials or structural members relevant to their own applications.

This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.

This work contains proceedings of a workshop on Bifurcation and Localisation Theory in Geomechanics, held in Perth, Australia in 1999. It covers a range of themes from classic civil engineering subjects to non-linear and non-unique geological phenomena.

This book offers an essential introduction to the linear and non-linear behavior of solid materials, and to the concepts of deformation, displacement and stress, within the context of continuum mechanics and thermodynamics. To illustrate the fundamental principles, the book starts with an overview of solid mechanics, experimental methods, classes of material behaviors, and the thermodynamic modeling framework. It then explores linear elastic behavior, thermoelasticity, plasticity, viscoplasticity, fracture mechanics and damage behavior. The last part of the book is devoted to conventional and magnetic shape memory alloys, which may be used as actuators or sensors in adaptive structures. Given its range of coverage, the book will be especially valuable for students of engineering courses in Mechanics. Further, it includes a wealth of examples and exercises, making it accessible to the widest possible audience.

This publication elucidates the various problems associated with attaining stability, and provides the results for practical use by the design engineer. By presenting a simple and visual description of the physical phenomena, the authors show how to determine the critical loads of various structures, such as frames, arches, building structures, trusses and sandwiches. Special emphasis is given to the post-critical behaviour - essential for assessing the safety of structures - and furthermore to the summation theories that make the solution of complicated stability problems relatively simple. It is a guide for structural design engineers and researchers who need a good understanding of buckling phenomena. It should also be a useful text for undergraduate and MSc students on structural stability courses.

This book casts new light on the process that in the sixteenth and seventeenth centuries led to a profound transformation in the study of nature with the emergence of mechanistic philosophy, the new mixed mathematics, and the establishment of the experimental approach. It is argued that modern European science originated from Hellenistic mathematics not so much because of rediscovery of the latter but rather because its "applied" components, namely mechanics, optics, harmonics, and astronomy, and their methodologies continued to be transmitted throughout the Middle Ages without serious interruption. Furthermore, it is proposed that these "applied" components played a role in their entirety; thus, for example, "new" mechanics derived not only from "old" mechanics but also from harmonics, optics, and astronomy. Unlike other texts on the subject, the role of mathematicians is stressed over that of philosophers of nature and the focus is particularly on epistemological aspects. In exploring Galilean and post-Galilean epistemology, attention is paid to the contributions of Galileo's disciples and also the impact of his enemies. The book will appeal to both historians of science and scientists.

Engineering Solid Mechanics bridges the gap between elementary approaches to strength of materials and more advanced, specialized versions on the subject.
The book provides a basic understanding of the fundamentals of elasticity and plasticity, applies these fundamentals to solve analytically a spectrum of engineering problems, and introduces advanced topics of mechanics of materials - including fracture mechanics, creep, superplasticity, fiber reinforced composites, powder compacts, and porous solids.

Text includes:
o stress and strain, equilibrium, and compatibility
o elastic stress-strain relations
o the elastic problem and the stress function approach to solving plane elastic problems
o applications of the stress function solution in Cartesian and polar coordinates
o Problems of elastic rods, plates, and shells through formulating a strain compatibility function as well as applying energy methods
o Elastic and elastic-plastic fracture mechanics
o Plastic and creep deformation
o Inelastic deformation and its applications
This book presents the material in an instructive manner, suitable for individual self-study. It emphasizes analytical treatment of the subject, which is essential for handling modern numerical methods as well as assessing and creating software packages. The authors provide generous explanations, systematic derivations, and detailed discussions, supplemented by a vast variety of problems and solved examples.
Primarily written for professionals and students in mechanical engineering, Engineering Solid Mechanics also serves persons in other fields of engineering, such as aerospace, civil, and material engineering.

This book provides structural reliability and design students with fundamental knowledge in structural reliability, as well as an overview of the latest developments in the field of reliability engineering. It addresses the mathematical formulation of analytical tools for structural reliability assessment. This book offers an accessible introduction to structural reliability assessment and a solid foundation for problem-solving. It introduces the topic and background, before dealing with probability models for random variables. It then explores simulation techniques for single random variables, random vectors consisting of different variables, and stochastic processes. The book addresses analytical approaches for structural reliability assessment, including the reliability models for a single structure and those for multiple structures, as well as discussing the approaches for structural time-dependent reliability assessment in the presence of discrete and continuous load processes. This book delivers a timely and pedagogical textbook, including over 170 worked-through examples, detailed solutions, and analytical tools, making it of interest to a wide range of graduate students, researchers, and practitioners in the field of reliability engineering.

One of the most important subjects for any student of engineering to master is the behaviour of materials and structures under load. The way in which they react to applied forces, the deflections resulting and the stresses and strains set up in the bodies concerned are all vital considerations when designing a mechanical component such that it will not fail under predicted load during its service lifetime.
All the essential elements of a treatment of these topics are contained within this course of study, starting with an introduction to the concepts of stress and strain, shear force and bending moments and moving on to the examination of bending, shear and torsion in elements such as beams, cylinders, shells and springs. A simple treatment of complex stress and complex strain leads to a study of the theories of elastic failure and an introduction to the experimental methods of stress and strain analysis.
More advanced topics are dealt with in a companion volume - Mechanics of Materials 2. Each chapter contains a summary of the essential formulae which are developed in the chapter, and a large number of worked examples which progress in level of difficulty as the principles are enlarged upon. In addition, each chapter concludes with an extensive selection of problems for solution by the student, mostly examination questions from professional and academic bodies, which are graded according to difficulty and furnished with answers at the end.
* Emphasis on practical learning and applications, rather than theory
* Provides the essential formulae for each individual chapter
* Contains numerous worked examples and problems

The mechanics of electromagnetic materials and structures has been developing rapidly with extensive applications in, e. g. , electronics industry, nuclear engineering, and smart materials and structures. Researchers in this interdisciplinary field are with diverse background and motivation. The Symposium on the Mechanics of Electromagnetic Materials and Structures of the Fourth International Conference on Nonlinear Mechanics in Shanghai, China in August 13-16, 2002 provided an opportunity for an intimate gathering of researchers and exchange of ideas. This volume contains papers based on most of the presentations at the symposium, and articles from a few invited contributors. These papers reflect some of the recent activities in the mechanics of electromagnetic materials and structures. The first twelve papers are in the order in which they were listed in the program of the conference. These are followed by six invited papers in alphabetical order of the last names of the first authors. We would like to extend our sincere thanks to Professor David Y. Gao of Virginia Tech for suggesting the symposium, and to the authors for their time and effort invested in preparing their manuscripts. We are also grateful to Professor Daining Fang of Tsinghua University for co-chairing the symposium with J. S. Yang. Our special thanks belong to Kluwer for preparing this book for publication. J. S. Yang G. A. Maugin PIEZOELECTRIC VIBRATORY GYROSCOPES J. S.

Concrete durability in climates where freezing and thawing occurs is a continuing problem. It is particularly acute for highway and bridge structures, where de-icing salts are used to combat the effects of frost, snow and ice. These salts can cause damage to concrete and accelerate corrosion of reinforcements. This book presents the latest international research on this area, with contributions from North America and Europe which were presented at an international RILEM workshop.

This work details general theories and reliable analysis techniques for solving real-world problems in linear and non-linear mechanics. This book looks at the structural and mechanical behaviour of components such as beams, frames and plates of both uniform and variable stiffness in terms of both stress and deformation. It also emphasizes the challenging demands of industry. College or university bookstores may order five or more copies at a special student price, available on request from Marcel Dekker, Inc.

This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory. The objective is to expose the most intriguing aspects of elasticity and viscoelasticity with finite strains in such a way as to ensure mathematical correctness, on the one hand, and to demonstrate a wide spectrum of physical phenomena typical only of nonlinear mechanics, on the other.A novel aspect of the book is that it contains a number of examples illustrating surprising behaviour in materials with finite strains, as well as comparisons between theoretical predictions and experimental data for rubber-like polymers and elastomers.The book aims to fill a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics. The book has been developed from a graduate course in applied mathematics which the author has given for a number of years.

Nonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics.
Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws.
The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations.

Unique in its approach, this introduction to the physics of creep concentrates on the physical principles underlying observed phenomena. As such it provides a resource for graduate students in materials science, metallurgy, mechanical engineering, physics and chemistry as well as researchers in other fields. Following a brief mathematical treatment, the authors introduce creep phenomena together with some empirical laws and observations. The mechanisms of creep and diffusion under varying experimental conditions are subsequently analysed and developed. The second half of the text considers alloying in greater detail as well as exploring the structure and properties of superalloys and stress effects in these materials.

Inelastic media constitute a rich source of interesting and important problems in theoretical, experimental and computationalmechanics. Signi?cantinsightshavebeengainedthroughstudiesofthemathematicalchar- teristics of new models. New constitutive theories have lead to variational and other formulations that are generally more complex, often highly nonlinear, and requ- ing new tools for their successful resolution. Likewise, there have been signi?cant advances of a computational nature, coupled to the development of new algorithms for solving such problems in discrete form. It is clear, therefore, that research in the broad area of inelastic media offers c- temporary investigators a range of challenges which are most fruitfully addressed througha combinationof theoretical, experimentaland computationalavenues.F- thermore, the ?eld is truly multidisciplinary in nature, drawing on the expertise of specialists in materials science, various branches of engineering, mathematics, and physics, and bene?ting from integrative approaches to the solution of problems. The objective of the IUTAM Symposium on Theoretical, Modelling and C- putational Aspects of Inelastic Media, held in Cape Town over the period 14-18 January 2008, was to provide a forum in which experts engaged in a spectrum of activities underthe theme of inelastic media could discussrecent developments, and also identify key open problem

This book discusses recent findings and advanced theories presented at two workshops at TU Berlin in 2017 and 2018. It underlines several advantages of generalized continuum models compared to the classical Cauchy continuum, which although widely used in engineering practice, has a number of limitations, such as: * The structural size is very small. * The microstructure is complex. * The effects are localized. As such, the development of generalized continuum models is helpful and results in a better description of the behavior of structures or materials. At the same time, there are more and more experimental studies supporting the new models because the number of material parameters is higher.

This book serves both as a textbook and a scientific work. As a textbook, the work gives a clear, thorough and systematic presentation of the fundamental postulates, theorems and principles and their applications of the classical mathematical theories of plasticity and creep. In addition to the mathematical theories, the physical theory of plasticity, the book presents the Budiansky concept of slip and its modification by M. Leonov. Special attention is given to the analysis of the advantages and shortcomings of the classical theories. In its main part, the book presents the synthetic theory of irreversible deformations, which is based on the mathematical Sanders flow plasticity theory and the physical theory, the Budiansky concept of slip. The main peculiarity of the synthetic theory is that the formulae for both plastic and creep deformation, as well their interrelations, can be derived from the single constitutive equation. Furthermore, the synthetic theory, as physical one, can take into account the real processes that take place in solids at irreversible deformation. This widens considerably the potential of the synthetic theory. In the framework of the synthetic theory such problems as creep delay, the Hazen-Kelly effect, the deformation at the break of the load trajectory, the influence of the rate of loading on the stress-strain diagram, creep at the changes of load, creep at unloading and reversed creep, have been analytically described. In the last chapter, the book shows the solution of some contemporary problems of plasticity and creep: Creep deformation at cyclic abrupt changes of temperature, The influence of irradiation on the plastic and creep deformation, Peculiarities of deformation at the phase transformation of some metals.

This book mainly introduces some basic phenomena and laws of highly ductile materials during elastoplastic deformation, and their engineering applications, such as the transfer and relief of stress concentration in the notch root, the mitigation of possible brittle fracture, the ductile deformation and damage, fatigue, energy absorption, plastic buckling, thermal stress problems, etc. It shows a number of revolutions in modern applications and design, which are beneficial to the safety of modern equipment, and improve applicability. In addition, the first three chapters of this book also briefly introduce the basic knowledge of elastoplastic deformation and analysis as a preliminary knowledge. This book can be used as a textbook for advanced undergraduate students and postgraduate in non-mechanics majors such as mechanical engineering, power, material or civil engineering, as well as scholars and engineers in related fields.

This book compiles techniques used to analyze composite structural elements ranging from beams through plates to stiffened shells. The content is suitable for graduate-level students with a basic background in mechanics of composite materials. Moreover, this book will be placed in an active spot on the bookshelves of composite structures designers as well as researchers.

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 volume reports the latest technological advances in polymeric composites and blends, reinforced polymeric and composite materials, and ceramics of engineering importance. It covers topics ranging from physical and mechanical properties testing and characterization to specialty composites.

This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present 6th edition is updated and revised with more explanations, additional examples and problems with solutions, together with new sections on applications in science. Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics. The book contains more than 150 problems with complete solutions, as well as some practical examples which make moderate use of personal computers. This will be appreciated in particular by students using this textbook to accompany lectures on mechanics. The book ends with some historical notes on scientists who made important contributions to the development of mechanics.

This book presents the bending theory of hyperelastic beams in the context of finite elasticity. The main difficulties in addressing this issue are due to its fully nonlinear framework, which makes no assumptions regarding the size of the deformation and displacement fields. Despite the complexity of its mathematical formulation, the inflexion problem of nonlinear beams is frequently used in practice, and has numerous applications in the industrial, mechanical and civil sectors. Adopting a semi-inverse approach, the book formulates a three-dimensional kinematic model in which the longitudinal bending is accompanied by the transversal deformation of cross-sections. The results provided by the theoretical model are subsequently compared with those of numerical and experimental analyses. The numerical analysis is based on the finite element method (FEM), whereas a test equipment prototype was designed and fabricated for the experimental analysis. The experimental data was acquired using digital image correlation (DIC) instrumentation. These two further analyses serve to confirm the hypotheses underlying the theoretical model. In the book's closing section, the analysis is generalized to the case of variable bending moment. The governing equations then take the form of a coupled system of three equations in integral form, which can be applied to a very wide class of equilibrium problems for nonlinear beams.

This is an intermediate book for beginning postgraduate students and junior researchers, and offers up-to-date content on both continuum mechanics and elasticity. The material is self-contained and should provide readers sufficient working knowledge in both areas. Though the focus is primarily on vector and tensor calculus (the so-called coordinate-free approach), the more traditional index notation is used whenever it is deemed more sensible. With the increasing demand for continuum modeling in such diverse areas as mathematical biology and geology, it is imperative to have various approaches to continuum mechanics and elasticity. This book presents these subjects from an applied mathematics perspective. In particular, it extensively uses linear algebra and vector calculus to develop the fundamentals of both subjects in a way that requires minimal use of coordinates (so that beginning graduate students and junior researchers come to appreciate the power of the tensor notation).