F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media.

Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones.
The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.

T. Wichtmann, T. Triantafyllidis: Behaviour of granular soils under environmentally induced cyclic loads. - D. Muir Wood: Constitutive modelling. - C. di Prisco: Creep versus transient loading effects in geotechnical problems. - M. Pastor et al.: Mathematical models for transient, dynamic and cyclic problems in geotechnical engineering. - M. Pastor: Discretization techniques for transient, dynamics and cyclic problems in geotechnical engineering: first order hyperbolic partial diffential equations. - M. Pastor et l.: Discretization techniques for transient, dynamic and cyclic problems in geotechnical engineering: second order equation. - C. di Prisco: Cyclic mechanical response of rigid bodies interacting with sand strata. - D. Muir Wood: Macroelement modelling. - M. F. Randolph: Offshore design approaches and model tests for sub-failure cyclic loading of foundations. - M.F. Randolph: Cyclic interface shearing in sand and cemented solis and application to axial response of piles. - M. F. Randolph: Evaluation of the remoulded shear strength of offshore clays and application to pipline-soil and riser-soil interaction.

The book gives a comprehensive description of the mechanical response of soils (granular and cohesive materials) under cyclic loading. It provides the geotechnical engineer with the theoretical and analytical tools necessary for the evaluation of settlements developng with time under cyclic, einvironmentally idncued loads (such as wave motion, wind actions, water table level variation) and their consequences for the serviceability and durability of structures such as the shallow or deep foundations used in offshore engineering, caisson beakwaters, ballast and airport pavements and also to interpret monitoring data, obtained from both natural and artificial slopes and earth embankments, for the purposes of risk assessment and mitigation.

Piezoelectricity has been a steadily growing field, with recent advances made by researchers from applied physics, acoustics, materials science, and engineering. This collective work presents a comprehensive treatment of selected advanced topics in the subject. The book is written for an intermediate graduate level and is intended for researchers, mechanical engineers, and applied mathematicians interested in the advances and new applications in piezoelectricity.

The purpose of this book is to bridge the gap between the traditional Geomechanics and Numerical Geotechnical Modelling with applications in science and practice. Geomechanics is rarely taught within the rigorous context of Continuum Mechanics and Thermodynamics, while when it comes to Numerical Modelling, commercially available finite elements or finite differences software utilize constitutive relationships within the rigorous framework. As a result, young scientists and engineers have to learn the challenging subject of constitutive modelling from a program manual and often end up with using unrealistic models which violate the Laws of Thermodynamics. The book is introductory, by no means does it claim any completeness and state of the art in such a dynamically developing field as numerical and constitutive modelling of soils. The author gives basic understanding of conventional continuum mechanics approaches to constitutive modelling, which can serve as a foundation for exploring more advanced theories. A considerable effort has been invested here into the clarity and brevity of the presentation. A special feature of this book is in exploring thermomechanical consistency of all presented constitutive models in a simple and systematic manner.

This volume presents results of the International Meshing Roundtable conference organized by Sandia National Laboratories held in September 2005. The conference is held annually and since its inception eleven years ago has become widely recognized as a major forum for the exchange of ideas in this field. The papers of this proceedings are devoted to mesh generation and adaptation which has applications to finite element simulation as well as to computational geometry and computer graphics. This book introduces theoretical and novel ideas with practical potential as well as technical applications from industrial researchers, bringing together renowned specialists from engineering, computer science and mathematics.

The concept of virtual manufacturing has been developed in order to increase the industrial performances, being one of the most ef cient ways of reducing the m- ufacturing times and improving the quality of the products. Numerical simulation of metal forming processes, as a component of the virtual manufacturing process, has a very important contribution to the reduction of the lead time. The nite element method is currently the most widely used numerical procedure for s- ulating sheet metal forming processes. The accuracy of the simulation programs used in industry is in uenced by the constitutive models and the forming limit curves models incorporated in their structure. From the above discussion, we can distinguish a very strong connection between virtual manufacturing as a general concept, ?nite element method as a numerical analysis instrument and constitutive laws,aswellas forming limit curves as a speci city of the sheet metal forming processes. Consequently, the material modeling is strategic when models of reality have to be built. The book gives a synthetic presentation of the research performed in the eld of sheet metal forming simulation during more than 20 years by the members of three international teams: the Research Centre on Sheet Metal Forming-CERTETA (Technical University of Cluj-Napoca, Romania); AutoForm Company from Zurich, Switzerland and VOLVO automotive company from Sweden. The rst chapter presents an overview of different Finite Element (FE) formu- tions used for sheet metal forming simulation, now and in the past.

Through his voluminous and in?uential writings, editorial activities, organi- tional leadership, intellectual acumen, and strong sense of history, Clifford - brose Truesdell III (1919-2000) was the main architect for the renaissance of - tional continuum mechanics since the middle of the twentieth century. The present collection of 42 essays and research papers pays tribute to this man of mathematics, science, and natural philosophy as well as to his legacy. The ?rst ?ve essays by B. D. Coleman, E. Giusti, W. Noll, J. Serrin, and D. Speiser were texts of addresses given by their authors at the Meeting in memory of Clifford Truesdell, which was held in Pisa in November 2000. In these essays the reader will ?nd personal reminiscences of Clifford Truesdell the man and of some of his activities as scientist, author, editor, historian of exact sciences, and principal founding member of the Society for Natural Philosophy. The bulk of the collection comprises 37 research papers which bear witness to the Truesdellian legacy. These papers cover a wide range of topics; what ties them together is the rational spirit. Clifford Truesdell, in his address upon receipt of a Birkhoff Prize in 1978, put the essence of modern continuum mechanics succinctly as "conceptual analysis, analysis not in the sense of the technical term but in the root meaning: logical criticism, dissection, and creative scrutiny.

This is an introduction to the mathematical basis of finite element analysis as applied to vibrating systems. Finite element analysis is a technique that is very important in modeling the response of structures to dynamic loads. Although this book assumes no previous knowledge of finite element methods, those who do have knowledge will still find the book to be useful. It can be utilised by aeronautical, civil, mechanical, and structural engineers as well as naval architects. This second edition includes information on the many developments that have taken place over the last twenty years. Existing chapters have been expanded where necessary, and three new chapters have been included that discuss the vibration of shells and multi-layered elements and provide an introduction to the hierarchical finite element method.

Fracture mechanics is a vast and growing field. This book develops the basic elements needed for both fracture research and engineering practice. The emphasis is on continuum mechanics models for energy flows and crack-tip stress- and deformation fields in elastic and elastic-plastic materials. In addition to a brief discussion of computational fracture methods, the text includes practical sections on fracture criteria, fracture toughness testing, and methods for measuring stress intensity factors and energy release rates. Class-tested at Cornell, this book is designed for students, researchers and practitioners interested in understanding and contributing to a diverse and vital field of knowledge.

This volume highlights the latest developments and trends in advanced materials and their properties, the modeling and simulation of non-classical materials and structures, and new technologies for joining materials. It presents the developments of advanced materials and respective tools to characterize and predict the material properties and behavior.

The book introduces the reader to the fundamentals of rock mechanics and to its application to economic construction in rock. Models describe the mechanical properties and the permeability of rock. Numerical methods for evaluating the stability of structures in rock are given to solve special problems related to tunnels, caverns, pressure tunnels, dam foundations and slopes. Methods for testing the rock mechanical properties are described. A number of case histories enable the reader to make use of the content in his or her own work.

This collection provides researchers and scientists with advanced analyses and materials design techniques in Biomaterials and presents mechanical studies of biological structures. In 16 contributions well known experts present their research on Stress and Strain Analysis, Material Properties, Fluid and Gas mechanics and they show related problems.

This monograph presents recent research findings on fracture properties and behavior of the composites, and their damage and cracking process under both quasi-static and impact loading conditions. Theoretical treatment, experimental investigation and numerical simulation aspects of the mechanics of composites, including sandwich structures are included.

The First African InterQuadrennial ICF Conference "AIQ-ICF2008" on Damage and Fracture Mechanics - Failure Analysis of Engineering Materials and Structures", Algiers, Algeria, June 1-5, 2008 is the first in the series of InterQuadrennial Conferences on Fracture to be held in the continent of Africa. During the conference, African researchers have shown that they merit a strong reputation in international circles and continue to make substantial contributions to the field of fracture mechanics. As in most countries, the research effort in Africa is und- taken at the industrial, academic, private sector and governmental levels, and covers the whole spectrum of fracture and fatigue. The AIQ-ICF2008 has brought together researchers and engineers to review and discuss advances in the development of methods and approaches on Damage and Fracture Mechanics. By bringing together the leading international experts in the field, AIQ-ICF promotes technology transfer and provides a forum for industry and researchers of the host nation to present their accomplishments and to develop new ideas at the highest level. International Conferences have an important role to play in the technology transfer process, especially in terms of the relationships to be established between the participants and the informal exchange of ideas that this ICF offers.

"Molecular Modeling and Multiscaling Issues for Electronic Material Applications" provides a snapshot on the progression of molecular modeling in the electronics industry and how molecular modeling is currently being used to understand material performance to solve relevant issues in this field. This book is intended to introduce the reader to the evolving role of molecular modeling, especially seen through the eyes of the IEEE community involved in material modeling for electronic applications. Part I presents the role that quantum mechanics can play in performance prediction, such as properties dependent upon electronic structure, but also shows examples how molecular models may be used in performance diagnostics, especially when chemistry is part of the performance issue. Part II gives examples of large-scale atomistic methods in material failure and shows several examples of transitioning between grain boundary simulations (on the atomistic level)and large-scale models including an example of the use of quasi-continuum methods that are being used to address multiscaling issues. Part III is a more specific look at molecular dynamics in the determination of the thermal conductivity of carbon-nanotubes. Part IV covers the many aspects of molecular modeling needed to understand the relationship between the molecular structure and mechanical performance of materials. Finally, Part V discusses the transitional topic of multiscale modeling and recent developments to reach the submicronscale using mesoscale models, including examples of direct scaling and parameterization from the atomistic to the coarse-grained particle level.
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Computational Methods in Elasticity and Plasticity: Solids and Porous Media presents the latest developments in the area of elastic and elasto-plastic finite element modeling of solids, porous media and pressure-dependent materials and structures. The book covers the following topics in depth: the mathematical foundations of solid mechanics, the finite element method for solids and porous media, the theory of plasticity and the finite element implementation of elasto-plastic constitutive models. The book also includes: -A detailed coverage of elasticity for isotropic and anisotropic solids. -A detailed treatment of nonlinear iterative methods that could be used for nonlinear elastic and elasto-plastic analyses. -A detailed treatment of a kinematic hardening von Mises model that could be used to simulate cyclic behavior of solids. -Discussion of recent advances in the analysis of porous media and pressure-dependent materials in more detail than other books currently available. Computational Methods in Elasticity and Plasticity: Solids and Porous Media also contains problem sets, worked examples and a solutions manual for instructors.

This book contains a collection of papers that were presented at the IUTAM Symposium on "Computer Models in Biomechanics: From Nano to Macro" held at Stanford University, California, USA, from August 29 to September 2, 2011. It contains state-of-the-art papers on: - Protein and Cell Mechanics: coarse-grained model for unfolded proteins, collagen-proteoglycan structural interactions in the cornea, simulations of cell behavior on substrates - Muscle Mechanics: modeling approaches for Ca2+-regulated smooth muscle contraction, smooth muscle modeling using continuum thermodynamical frameworks, cross-bridge model describing the mechanoenergetics of actomyosin interaction, multiscale skeletal muscle modeling - Cardiovascular Mechanics: multiscale modeling of arterial adaptations by incorporating molecular mechanisms, cardiovascular tissue damage, dissection properties of aortic aneurysms, intracranial aneurysms, electromechanics of the heart, hemodynamic alterations associated with arterial remodeling following aortic coarctation, patient-specific surgery planning for the Fontan procedure - Multiphasic Models: solutes in hydrated biological tissues, reformulation of mixture theory-based poroelasticity for interstitial tissue growth, tumor therapies of brain tissue, remodeling of microcirculation in liver lobes, reactions, mass transport and mechanics of tumor growth, water transport modeling in the brain, crack modeling of swelling porous media - Morphogenesis, Biological Tissues and Organs: mechanisms of brain morphogenesis, micromechanical modeling of anterior cruciate ligaments, mechanical characterization of the human liver, in vivo validation of predictive models for bone remodeling and mechanobiology, bridging scales in respiratory mechanics

By drawing together the current theoretical and experimental understanding of the phenomena of delayed hydride cracking (DHC) in zirconium alloys, The Effect of Hydrogen and Hydrides on the Integrity of Zirconium Alloy Components: Delayed Hydride Cracking provides a detailed explanation focusing on the properties of hydrogen and hydrides in these alloys. Whilst the emphasis lies on zirconium alloys, the combination of both the empirical and mechanistic approaches creates a solid understanding that can also be applied to other hydride forming metals. This up-to-date reference focuses on documented research surrounding DHC, including current methodologies for design and assessment of the results of periodic in-service inspections of pressure tubes in nuclear reactors. Emphasis is placed on showing how our understanding of DHC is supported by progress in general understanding of such broad fields as the study of hysteresis associated with first order phase transformations, phase relationships in coherent crystalline metallic solids, the physics of point and line defects, diffusion of substitutional and interstitial atoms in crystalline solids, and continuum fracture and solid mechanics. Furthermore, an account of current methodologies is given illustrating how such understanding of hydrogen, hydrides and DHC in zirconium alloys underpins these methodologies for assessments of real life cases in the Canadian nuclear industry. The all-encompassing approach makes The Effect of Hydrogen and Hydrides on the Integrity of Zirconium Alloy Component: Delayed Hydride Cracking an ideal reference source for students, researchers and industry professionals alike.

This book contains a systematical analysis of geometrical situations leading to contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface. Each contact pair is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system. The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are then ready-for-implementation numerical algorithms within the finite element method including any arbitrary discretization techniques such as high order and isogeometric finite elements, which are most convenient for the considered geometrical situation. The book proposes a consistent study of geometry and kinematics, variational formulations, constitutive relations for surfaces and discretization techniques for all considered geometrical pairs and contains the associated numerical analysis as well as some new analytical results in contact mechanics.

As structural elements, anisotropic elastic plates find wide applications in modern technology. The plates here are considered to be subjected to not only inplane load but also transverse load. In other words, both plane and plate bending problems as well as the stretching-bending coupling problems are all explained in this book. In addition to the introduction of the theory of anisotropic elasticity, several important subjects have are discussed in this book such as interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermoelastic problems and boundary element analysis.

The book contains 26 scientific contributions by leading experts from Russia, Austria, Italy, Japan and Taiwan. It presents an overview on recent developments in Advanced Dynamics and Model Based Control of Structures and Machines. Main topics are nonlinear control of structures and systems, sensing and actuation, active and passive damping, nano- and micromechanics, vibrations and waves.

This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his 60th birthday. It contains contributions from friends and collaborators as well as current and former PhD students from almost all continents. As a very diverse group of people, the authors cover a wide range of topics from fundamental research to industrial applications: contact mechanics, finite element technology, micromechanics, multiscale approaches, particle methods, isogeometric analysis, stochastic methods and further research interests. In summary, the volume presents an overview of the international state of the art in computational mechanics, both in academia and industry.

This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

Engineering mechanics involves the development of mathematical models of the physical world. Statics addresses the forces acting on and in mechanical objects and systems. Statics with MATLAB (R) develops an understanding of the mechanical behavior of complex engineering structures and components using MATLAB (R) to execute numerical calculations and to facilitate analytical calculations. MATLAB (R) is presented and introduced as a highly convenient tool to solve problems for theory and applications in statics. Included are example problems to demonstrate the MATLAB (R) syntax and to also introduce specific functions dealing with statics. These explanations are reinforced through figures generated with MATLAB (R) and the extra material available online which includes the special functions described. This detailed introduction and application of MATLAB (R) to the field of statics makes Statics with MATLAB (R) a useful tool for instruction as well as self study, highlighting the use of symbolic MATLAB (R) for both theory and applications to find analytical and numerical solutions

This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, .say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation."