Emphasising non-penetrating collisions, the second edition of Impact Mechanics develops several different methodologies for analysing collisions between structures - from rigid body theory for structures that are stiff and compact, to vibration and wave analyses for flexible structures. A valuable reference for both professionals and advanced undergraduate and graduate students, the book builds upon foundation courses in dynamics and strength of materials. Worked examples and end-of-chapter homework problems are drawn both from industry and sports such as golf, baseball, soccer and billiards. New chapters present a generalised theory of multi-body impact, as well as analyses of visco-elastic and visco-plastic impact. Effects of local compliance on impact dynamics are more generally described, and additional examples illustrating effects of friction during impact between bodies in either collinear or eccentric configurations are included.

Geodynamics is the study of the deformation and flow of the solid Earth and other planetary interiors. Focusing on the Earth's mantle, this book provides a comprehensive, mathematically advanced treatment of the continuum mechanics of mantle processes and the craft of formulating geodynamical models to approximate them. Topics covered include slow viscous flow, elasticity and viscoelasticity, boundary-layer theory, long-wave theories including lubrication theory and shell theory, two-phase flow, and hydrodynamic stability and thermal convection. A unifying theme is the utility of powerful general methods (dimensional analysis, scaling analysis, and asymptotic analysis) that can be applied in many specific contexts. Featuring abundant exercises with worked solutions for graduate students and researchers, this book will make a useful resource for Earth scientists and applied mathematicians with an interest in mantle dynamics and geodynamics more broadly.

All metallic materials are prepared from the liquid state as their parent phase. Solidification is therefore one of the most important phase transformation in daily human life. Solidification is the transition from liquid to solid state of matter. The conditions under which material is transformed determines the physical and chemical properties of the as-solidified body. The processes involved, like nucleation and crystal growth, are governed by heat and mass transport.
Convection and undercooling provide additional processing parameters to tune the solidification process and to control solid material performance from the very beginning of the production chain.
To develop a predictive capability for efficient materials production the processes involved in solidification have to be understood in detail.
This book provides a comprehensive overview of the solidification of metallic melts processed and undercooled in a containerless manner
by drop tube, electromagnetic and electrostatic levitation, and experiments in reduced gravity.
The experiments are accompanied by model calculations on the influence of thermodynamic and hydrodynamic conditions that control
selection of nucleation mechanisms and modify crystal growth development throughout the solidification process.

This book focuses on the development of a new simulation paradigm allowing for the solution of models that up to now have never been resolved and which result in spectacular CPU time savings (in the order of millions) that, combined with supercomputing, could revolutionize future ICT (information and communication technologies) at the heart of science and technology. The authors have recently proposed a new paradigm for simulation-based engineering sciences called Proper Generalized Decomposition, PGD, which has proved a tremendous potential in many aspects of forming process simulation. In this book a review of the basics of the technique is made, together with different examples of application.

This book introduces a trans-scale framework necessary for the physical understanding of breakdown behaviors and presents some new paradigm to clarify the mechanisms underlying the trans-scale processes. The book, which is based on the interaction of mechanics and statistical physics, will help to deepen the understanding of how microdamage induces disaster and benefit the forecasting of the occurrence of catastrophic rupture. It offers notes and problems in each part as interesting background and illustrative exercises. Readers of the book would be graduate students, researchers, engineers working on civil, mechanical and geo-engineering, etc. However, people with various background but interested in disaster reduction and forecasting, like applied physics, geophysics, seismology, etc., may also be interested in the book.

This book provides a concise discussion of fatigue crack growth (FCG) failure and lifing analysis methods for metallic aircraft structures and components. After a reasonably concise historical review, surveys are made of (i) the importance of fatigue for aircraft structural failures and the sources of fatigue nucleation and cracking, (ii) contemporary FCG lifing methods, and (iii) the Quantitative Fractography (QF) required for determining the actual FCG behaviour. These surveys are followed by the main part of the book, which is a discussion, using case histories, of the applicabilities of Linear Elastic Fracture Mechanics (LEFM) and non-LEFM methods for analysing service fatigue failures and full- and sub-scale test results. This discussion is derived primarily from the experiences of the Defence Science and Technology Group in Melbourne, Australia, and the Netherlands Aerospace Centre, Marknesse, the Netherlands.

This SpringerBrief covers the main scales of description of matter, starting at its finest level, the quantum scale, moving through ab-initio, molecular dynamics, coarse grained approaches, to finish at the scale of kinetic theory models that allows a nice compromise between the rich but expensive microscopic descriptions and the computationally cheap but sometimes too coarse macroscopic descriptions. The book addresses undergraduate and graduate students, as well as beginners in multi-scale modeling of materials.

Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations.

This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.

This book of recommendations presents an overview of High Frequency Mechanical Impact (HFMI) techniques existing today in the market and their proper procedures, quality assurance measures and documentation. Due to differences in HFMI tools and the wide variety of potential applications, certain details of proper treatments and quantitative quality control measures are presented generally. An example of procedure specification as a quality assurance measure is given in the Appendix. Moreover, the book presents procedures for the fatigue life assessment of HFMI-improved welded joints based on nominal stress, structural hot spot stress and effective notch stress. It also considers the extra benefit that has been experimentally observed for HFMI-treated high-strength steels. The recommendations offer proposals on the effect of loading conditions like high mean stress fatigue cycles, variable amplitude loading and large amplitude/low cycle fatigue cycles. Special considerations for low stress concentration welded joints are also given. In order to demonstrate the use of the guideline, the book provides several fatigue assessment examples.

This is the first comprehensive volume on nearly periodic structures and mistuned blade vibration. Alok Sinha presents fundamental concepts and state-of-the-art techniques in the analysis of free and forced response of a nearly periodic structure, weaving together his own work (covering thirty-five years of research in this field) with works by other researchers. He also discusses similarities between tools used in bladed rotor analysis and condensed matter physics. Specific subjects covered include the reasons behind mode localization, the reasons behind amplitude amplification of steady-state response, state-of-the-art computational techniques for mistuned bladed rotors including multistage rotors, identification of mistuning from measured response, vibration localization in linear atomic chains, and analysis of two-dimensional periodic structures.

This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. Please visit the author's website for supplemental material, including PowerPoint presentations and MATLAB codes, at http://www2.mae.ufl.edu/nkim/INFEM/

A wide variety of applications ranging from microelectronics to turbines for propulsion and power generation rely on films, coatings, and multilayers to improve performance. As such, the ability to predict coating failure - such as delamination (debonding), mud-cracking, blistering, crack kinking, and the like - is critical to component design and development. This work compiles and organizes decades of research that established the theoretical foundation for predicting such failure mechanisms, and clearly outlines the methodology needed to predict performance. Detailed coverage of cracking in multilayers is provided, with an emphasis on the role of differences in thermoelastic properties between the layers. The comprehensive theoretical foundation of the book is complemented by easy-to-use analysis codes designed to empower novices with the tools needed to simulate cracking; these codes enable not only precise quantitative reproduction of results presented graphically in the literature, but also the generation of new results for more complex multilayered systems.

This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his 70th birthday. Thanks to his high dedication to research, over the years Peter Wriggers has built an international network with renowned experts in the field of computational mechanics. This is proven by the large number of contributions from friends and collaborators as well as former PhD students from all over the world. The diversity of Peter Wriggers network is mirrored by the range of topics that are covered by this book. To name only a few, these include contact mechanics, finite & virtual element technologies, micromechanics, multiscale approaches, fracture mechanics, isogeometric analysis, stochastic methods, meshfree and particle methods. Applications of numerical simulation to specific problems, e.g. Biomechanics and Additive Manufacturing is also covered. The volume intends to present an overview of the state of the art and current trends in computational mechanics for academia and industry.

This text presents the techniques for a wide set of applications, ranging from the problems of size and shape optimization (historically the first to be studied) to topology and material optimization. Structural models are considered that use both discrete and finite elements. Structural materials can be classical or new. Emerging methods are also addressed, such as automatic differentiation, intelligent structures optimization, integration of structural optimization in concurrent engineering environments, and multidisciplinary optimization. This text should be of interest to researchers and designers in industries such as aerospace, automotive, mechanical, civil, nuclear, naval and offshore. It provides a reference for advanced undergraduate or graduate courses on structural optimization and optimum design.

This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklos Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.'s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.

This volume demonstrates the use of FORTRAN for numerical computing in the context of the finite element method. FORTRAN is still an important programming language for computational mechanics and all classical finite element codes are written in this language, some of them even offer an interface to link user-code to the main program. This feature is especially important for the development and investigation of new engineering structures or materials. Thus, this volume gives a simple introduction to programming of elasto-plastic material behavior, which is, for example, the prerequisite for implementing new constitutive laws into a commercial finite element program.

This book covers the impact of sustainable masonry on the environment, touting the many benefits of utilizing local and/or low embodied energy materials in the construction of sustainable buildings. .

This textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale. Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics. Among others this includes statistical mechanics (separate chapter), quantum mechanics, space flight, galactic dynamics, friction, and vibration spectroscopy. An introductory chapter compiles all essential mathematical tools, ranging from coordinates to complex numbers. Completely solved problems and examples facilitate a thorough understanding of the material.

This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals and results will be checked against experimental data.

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.

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.

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 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 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.