Designing new structural materials, extending lifetimes and guarding against fracture in service are among the preoccupations of engineers, and to deal with these they need to have command of the mechanics of material behaviour. The first volume of this two-volume work deals with elastic and elastoplastic behaviour; this second volume continues with viscoelasticity, damage, fracture (resistance to cracking) and contact mechanics. As in Volume I, the treatment starts from the active mechanisms on the microscopic scale and develops the laws of macroscopic behaviour. Chapter I deals with viscoplastic behaviour, as shown, for example, at low temperatures by the effects of oscillatory loads and at high temperatures by creep under steady load. Chapter 2 treats damage phenomena encountered in all materials - for example, metals, polymers, glasses, concretes - such as cavitation, fatigue and stress-corrosion cracking. Chapter 3 treats those concepts of fracture mechanics that are needed for the understanding of resistance to cracking and Chapter 4 completes the volume with a survey of the main concepts of contact mechanics. As with Volume I, each chapter has a set of exercises, either with solutions or with indications of how to attack the problem; and there are many explanatory diagrams and other illustrations.

The symposiumwas motivatedby theincreasing need for modelling of material behaviourundervarious mechan icalconditions. This need is driven by the evolut ion ofcomputer capac ityand the resulting ability for engineers and scien tiststo address complexproblems . Reliable models formaterialbehaviour, including accurate numericalvalues of parameters ,are necessary for a continued beneficial development ofthe computational side of solid mechanics .High rate plasticity ,thermally assisted creep and phasetransformationsare only a fewexamplesof areas where more accurate modelsare needed. Experiments are necessary for the establishment ofmodels and parameters , and modified versionsof conventional test methods can make important contributions . Also modern optical methodsoffer a highpotentialfor futureexperimental development. Numerical simulations ofexperiments and so-called inverse modelling arealso frequentlyused techniques. The aim of the symposium was to bring together researchers with an interest in the areaofexperimental and computational aspects ofmaterial modelling for exchange and discussionofpromising methodsandresults. Abisko,a national park in the Swedish mountain district about 200 km north of the arctic circle and about one hourve dri from the airport ofKiruna,was chosen for the symposium. The tourist hotel in the park , overlookinga beautiful lake , offered a suitablevenue for the symposium. This environment with tracks for short walks (and long hikes),goals for small excursions and a hotel with restaurant and bar ve the ga delegatesmany opportunitiesto meet , socialiseand discuss during breaks and evenings.

In this thesis, the author considers quantum gravity to investigate the mysterious origin of our universe and its mechanisms. He and his collaborators have greatly improved the analyticity of two models: causal dynamical triangulations (CDT) and n-DBI gravity, with the space-time foliation which is one common factor shared by these two separate models.

In the first part, the analytic method of coupling matters to CDT in 2-dimensional toy models is proposed to uncover the underlying mechanisms of the universe and to remove ambiguities remaining in CDT. As a result, the wave function of the 2-dimensional universe where matters are coupled is derived. The behavior of the wave function reveals that the Hausdorff dimension can be changed when the matter is non-unitary.

In the second part, the n-DBI gravity model is considered. The author mainly investigates two effects driven by the space-time foliation: the appearance of a new conserved charge in black holes and an extra scalar mode of the graviton. The former implies a breakdown of the black-hole uniqueness theorem while the latter does not show any pathological behavior.

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Non-Linear Field Theories of Mechanics has become a classic treatise in the field of continuum mechanics. Originally published nearly forty years ago, it probably has influenced practically all subsequent monographs on the subject. Its main parts are: - The General Theory of Material Behavior - Elasticity - Fluidity This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monograph’s genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also greatly contributed to the unification and standardization of the concepts, terms and notations in the field.

This book presents a unified hierarchical formulation of theories for three-dimensional continua, two-dimensional shells, one-dimensional rods, and zero-dimensional points. It allows readers with varying backgrounds easy access to fundamental understanding of these powerful Cosserat theories.

The book presents a history of classical mechanics by focusing on issues of equilibrium. The historical point of view adopted here restricts attention to cases where the effectiveness of forces is assessed on the basis of the virtual motion of their points of application. For completeness, hints of the alternative approach are also referred, the Archimedean for ancient mechanics and the Newtonian for modern mechanics. The laws resulting from consideration of virtual motions are named laws of virtual work. The modern formulations of the principle of virtual work are only a particular form of them. The book begins with the first documented formulations of laws of virtual work in the IV century BC in Greece and proceeds to the end of the XIX century AD in Europe. A significant space is devoted to Arabic and Latin mechanics of Middle Ages. With the Renaissance it began to appear slightly different wordings of the laws, which were often proposed as unique principles of statics. The process reached its apex with Bernoulli and Lagrange in the XVIII century. The book ends with some chapters dealing with the discussions that took place in the French school on the role of the Lagrangian version of the law of virtual work and its applications to continuum mechanics.

All phenomena in nature are characterized by motion. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion. In the study of a science of nature, mathematics plays an important role. Mechanics is the first science of nature which has been expressed in terms of mathematics, by considering various mathematical models, associated to phenomena of the surrounding nature. Thus, its development was influenced by the use of a strong mathematical tool. As it was already seen in the first two volumes of the present book, its guideline is precisely the mathematical model of mechanics. The classical models which we refer to are in fact models based on the Newtonian model of mechanics, that is on its five principles, i.e.: the inertia, the forces action, the action and reaction, the independence of the forces action and the initial conditions principle, respectively. Other models, e.g., the model of attraction forces between the particles of a discrete mechanical system, are part of the considered Newtonian model. Kepler's laws brilliantly verify this model in case of velocities much smaller then the light velocity in vacuum."

This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or even the heart muscle, to name but a few. The book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.

Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincare maps, Floquet theory, the Poincare-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.

Nonsmoothness and nonconvexity arise in numerous applications of mechan- ics and modeling due to the need for studying more and more complicated phe- nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap- plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical questions. Because of the upsurge in activity in the area of nonsmooth and noncon- vex mechanics, Professors Gao and Ogden, together with the late Professor P.D. Panagiotopoulos, had planned to organize a Minisymposium with the title Nonsmooth and Nonconvex Mechanics within the ASME 1999 Mechanics & Materials Conference, June 27-30 1999, Blacksburg, Virginia. After the unex- pected death of Professor Panagiotopoulos the first two editors invited the third editor (Professor Stavroulakis) to join them. A large number of mathematical and engineering colleagues supported our efforts by presenting lectures at the Minisymposium in which the available mathematical methods were described and many problems of nonsmooth and nonconvex mechanics were discussed. The interest of the many participants encourages us all to continue our research efforts.

This book is intended for first year physics graduate students who wish to learn about analytical mechanics. Lagrangians and Hamiltonians are extensively treated following chapters where particle motion, oscillations, coordinate systems, and rigid bodies are dealt with in far greater detail than in most undergraduate textbooks. Perturbation theory, relativistic mechanics, and two case studies of continuous systems are presented.Each subject is approached at progressively higher levels of abstraction. Lagrangians and Hamiltonians are first presented in an inductive way, leading up to general proofs. Hamiltonian mechanics is expressed in Cartan's notation not too early; there is a self-contained account of the traditional formulation.Numerous problems with detailed solutions are provided. Graduate students studying for the qualifying examination will find them very useful.

Unlike other books on this subject, which tend to concentrate on 2-D dynamics, this text focuses on the application of Newton-Euler methods to complex, real-life 3-D dynamics problems. It is thus ideal for elective courses in intermediate dynamics.

Our everyday life is in?uenced by many unexpected (dif?cult to predict) events usually referred as a chance. Probably, we all are as we are due to the accumulation point of a multitude of chance events. Gambling games that have been known to human beings nearly from the beginning of our civilization are based on chance events. These chance events have created the dream that everybody can easily become rich. This pursuit made gambling so popular. This book is devoted to the dynamics of the mechanical randomizers and we try to solve the problem why mechanical device (roulette) or a rigid body (a coin or a die) operating in the way described by the laws of classical mechanics can behave in such a way and produce a pseudorandom outcome. During mathematical lessons in primary school we are taught that the outcome of the coin tossing experiment is random and that the probability that the tossed coin lands heads (tails) up is equal to 1/2. Approximately, at the same time during physics lessons we are told that the motion of the rigid body (coin is an example of suchabody)isfullydeterministic. Typically,studentsarenotgiventheanswertothe question Why this duality in the interpretation of the simple mechanical experiment is possible? Trying to answer this question we describe the dynamics of the gambling games based on the coin toss, the throw of the die, and the roulette run.

This volume is devoted to the exciting topic of dissipative solitons, i.e. pulses or spatially localised waves in systems exhibiting gain and loss. Examples are laser systems, nonlinear resonators and optical transmission lines. The physical principles and mathematical concepts are explained in a clear and concise way, suitable for students and young researchers. The similarities and differences in the notion of a soliton between dissipative systems and Hamiltonian and integrable systems are discussed, and many examples are given. The contributions are written by the world's leading experts in the field, making it a unique exposition of this emerging topic.

In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion. Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure. With alternative derivations and proofs of established results substituted for those in the standard literature, this work serves as an important source for researchers, students and teachers.Skillfully combining in-depth mathematics and actual physical applications, this book will be of interest to the applied mathematician, the theoretical mechanical engineer and the dynamical astronomer alike.

This book presents research advances in the field of Continuous Media with Microstructure and considers the three complementary pillars of mechanical sciences: theory, research and computational simulation. It focuses on the following problems: thermodynamic and mathematical modeling of materials with extensions of classical constitutive laws, single and multicomponent media including modern multifunctional materials, wave propagation, multiscale and multiphysics processes, phase transformations, and porous, granular and composite materials. The book presents the proceedings of the 2nd Conference on Continuous Media with Microstructure, which was held in 2015 in Lagow, Poland, in memory of Prof. Krzysztof Wilmanski.

This book will reveal cost reductions and how to slash your energy costs without investing big money. The three pillars of costs reduction will discussed: Assembling your options and analyzing your risk; developing options with your utility; and cutting out obvious waste in your operation. Those who will benefit from this excellent text are business owners, CFOs, plant managers, plant engineers, and energy managers. You will learn how to distill what savings are possible and how you can quickly accomplish those savings from what you already know and can expect to walk away at the end of this book with confidence and a realistic plan of action for reducing your costs.

Combustion systems are confined fields of compressible fluids where exothermic processes of combustion take place, subject to boundary conditions imposed at its borders. The subject of Dynamics of Combustion Systems is presented in three parts:

Part 1. Exothermicity considering the thermodynamic effects due to evolution of exothermic energy in a combustion system

Chapter 1. Thermodynamic Aspects
Chapter 2. Evolutionary Aspects
Chapter 3. Heat Transfer Aspects
Chapter 4. Chemical Kinetic Aspects

Part 2. Field exposing the dynamic properties of flow fields where the exothermic energy is deposited

Chapter 5. Aerodynamic Aspects
Chapter 6. Random Vortex Method
Chapter 7. Gasdynamic Aspects
Chapter 8. Gasdynamic Fronts

Part 3. Explosions revealing the dynamic features of fields and fronts due to rapid deposition of exothermic energy

Chapter 9. Blast Wave Theory
Chapter 10. Self-Similar Solution
Chapter 11. Phase Space Method
Chapter 12. Detonation

Presenting some of the most recent results of Russian research into shock compression, as well as historical overviews of the Russian research programs into shock compression, this volume will provide Western researchers with many novel ideas and points of view. The chapters in this volume are written by leading Russian specialists various fields of high-pressure physics and form accounts of the main researches on the behavior of matter under shock-wave interaction. The experimental portions contain results of studies of shock compression of metals to high and ultra-high pressure, shock initiation of polymorphic transformations, strength, fracture and fragmentation under shock compression, and detonation of condensed explosives. There are also chapters on theoretical investigations of shock-wave compression and plasma states in regimes of high-pressure and high- temperature. The topics of the book are of interest to scientists and engineers concerned with questions of material behavior under impulsive loading and to the equation of state of matter. Application is to questions of high-speed impact, inner composition of planets, verification of model representations of material behavior under extreme 1oading conditions, syntheses of new materials, development of new technologies for material processing, etc. Russian research differs from much of the Western work in that it has traditionally been wider-ranging and more directed to extremes of response than to precise characterization of specific materials and effects. Western scientists could expect to benefit from the perspective gained from close knowledge of the Russian work.

This book begins with an introductory chapter summarizing the history of fluid mechanics. It then moves on to the essential mathematics and physics needed to understand and work in fluid mechanics. Analytical treatments are based on the Navier-Stokes equations.

These proceedings present an up-to-date and comprehensive review of the field of theoretical and applied mechanics. All the papers are written by leading experts presently active in this subject area.

Friction force microscopy is an important analytical tool in the field of tribology on the nanometer-scale. The contact area between the probing tip and the sample is reduced to some square nanometers, corresponding to the ideal of a single asperity contact. Traditional concepts, such as friction coefficients, adhesion and elasticity and stick-slip are re-examined with this novel technique. New concepts based upon classical and quantum mechanics are investigated.

Key Features: Describes feedstock evaluation and the effects of elemental, chemical and fractional composition. Details reactor types and bed types. Explores the process options and parameters involved. Assesses coke formation and additives. Considers next generation processes and developments.

This book deals with theoretical aspects of modelling the mechanical behaviour of manufacturing, processing, transportation or other systems in which the processed or supporting material is travelling through the system. Examples of such applications include paper making, transmission cables, band saws, printing presses, manufacturing of plastic films and sheets, and extrusion of aluminium foil, textiles and other materials.

The work focuses on out-of-plane dynamics and stability analysis for isotropic and orthotropic travelling elastic and viscoelastic materials, with and without fluid-structure interaction, using analytical and semi-analytical approaches. Also topics such as fracturing and fatigue are discussed in the context of moving materials. The last part of the book deals with optimization problems involving physical constraints arising from the stability and fatigue analyses, including uncertainties in the parameters.

The book is intended for researchers and specialists in the field, providing a view of the mechanics of axially moving materials. It can also be used as a textbook for advanced courses on this specific topic. Considering topics related to manufacturing and processing, the book can also be applied in industrial mathematics.
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