Download or read book Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory written by Julian Braun and published by Logos Verlag Berlin GmbH. This book was released on 2016-11-15 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear elastic behavior of solid materials is often described in the context of continuum mechanics. Alternatively, one can try to determine the behavior of every single atom in the material. Classically, the connection between these two types of models is made with the Cauchy-Born rule. The aim of this book is to provide good criteria for the Cauchy-Born rule to be true and to make the connection between continuum and atomistic models precise. In particular, this includes rigorous proofs for the existence of solutions to the atomistic boundary value problem and their convergence to the corresponding continuum solutions in the limit of small interatomic distances.
Download or read book Mathematical Elasticity written by Philippe G. Ciarlet and published by SIAM. This book was released on 2022-01-22 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.
Download or read book Global Regularity and Uniqueness of Solutions in a Surface Growth Model Using Rigorous A Posteriori Methods written by Christian Nolde and published by Logos Verlag Berlin GmbH. This book was released on 2017 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of rigorous numerical methods to approach problems which can not be solved using standard methods (yet) has increased signifiantly in recent years. In this book, riogorous a-posteriori methods are used to study the time evolution of a surface growth model, given by a fourth order semi-linear parabolic partial differential equation, where standard methods fail to verify global uniqueness and smoothness of solutions. Based on an arbitrary numerical approximation, a-posteriori error-analysis is applied in order to prevent a blow up analytically. This is a method that in a similar way also applies to the three dimensional Navier-Stokes equations. The main idea consists of energy-estimates for the error between solution and approximation that yields a scalar differential equation controlling the norm of the error with coefficients depending solely on the numerical data. This allows the solution of the differential equation to be bounded using only numerical data. A key technical tool is a rigorous eigenvalue bound for the nonlinear operator linearized around the numerical approximation. The presented method succeeds to show global uniqueness for relatively large initial conditions, which is demonstrated in many numerical examples.
Download or read book Nonlocal Modeling Analysis and Computation written by Qiang Du and published by SIAM. This book was released on 2019-03-20 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
Download or read book Linear and Nonlinear Waves in Microstructured Solids written by Igor V. Andrianov and published by CRC Press. This book was released on 2021-04-22 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.
Download or read book Principles of Multiscale Modeling written by Weinan E and published by Cambridge University Press. This book was released on 2011-07-07 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic discussion of the fundamental principles, written by a leading contributor to the field.
Download or read book Multiscaling in Molecular and Continuum Mechanics Interaction of Time and Size from Macro to Nano written by G.C. Sih and published by Springer Science & Business Media. This book was released on 2007-11-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time, a book is being edited to address how results from one scale can be shifted or related to another scale, say from macro to micro or vice versa. The new approach retains the use of the equilibrium mechanics within a scale level such that cross scale results can be connected by scale invariant criteria. Engineers in different disciplines should be able to understand and use the results.
Download or read book First Principles Approaches to Metals Alloys and Metallic Compounds written by Richard Dronskowski and published by MDPI. This book was released on 2018-11-26 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: (This book is a printed edition of the Special Issue "First-Principles Approaches to Metals, Alloys, and Metallic Compounds" that was published in Metals
Download or read book Effective Theories for Brittle Materials written by Manuel Friedrich and published by Logos Verlag Berlin GmbH. This book was released on 2015-07-20 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough understanding of crack formation in brittle materials is of great interest in both experimental sciences and theoretical studies. Such materials show an elastic response to very small displacements and develop cracks already at moderately large strains. Typically there is no plastic regime in between the restorable elastic deformations and complete failure due to fracture. The main focus of this book lies on the derivation of effective models for brittle materials in the simultaneous passage from discrete-to-continuum and nonlinear to linearized systems. In the first part the cleavage behavior of brittle crystals is investigated including the identification of critical loads for failure and the analysis of the geometry of crack paths that occur in the fractured regime. In the second part Griffith functionals in the realm of linearized elasticity are derived from nonlinear and frame indifferent energies by means of a quantitative geometric rigidity result for special functions of bounded deformation.
Download or read book Advances in Applied Mechanics written by and published by Academic Press. This book was released on 1998-10-29 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly acclaimed series provides survey articles on the present state and future direction of research in important branches of applied mechanics.
Download or read book Handbook of Peridynamic Modeling written by Florin Bobaru and published by CRC Press. This book was released on 2016-11-03 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on integration of interactions rather than spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.
Download or read book Modeling and Simulation for Microelectronic Packaging Assembly written by Shen Liu and published by John Wiley & Sons. This book was released on 2011-05-17 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although there is increasing need for modeling and simulation in the IC package design phase, most assembly processes and various reliability tests are still based on the time consuming "test and try out" method to obtain the best solution. Modeling and simulation can easily ensure virtual Design of Experiments (DoE) to achieve the optimal solution. This has greatly reduced the cost and production time, especially for new product development. Using modeling and simulation will become increasingly necessary for future advances in 3D package development. In this book, Liu and Liu allow people in the area to learn the basic and advanced modeling and simulation skills to help solve problems they encounter. Models and simulates numerous processes in manufacturing, reliability and testing for the first time Provides the skills necessary for virtual prototyping and virtual reliability qualification and testing Demonstrates concurrent engineering and co-design approaches for advanced engineering design of microelectronic products Covers packaging and assembly for typical ICs, optoelectronics, MEMS, 2D/3D SiP, and nano interconnects Appendix and color images available for download from the book's companion website Liu and Liu have optimized the book for practicing engineers, researchers, and post-graduates in microelectronic packaging and interconnection design, assembly manufacturing, electronic reliability/quality, and semiconductor materials. Product managers, application engineers, sales and marketing staff, who need to explain to customers how the assembly manufacturing, reliability and testing will impact their products, will also find this book a critical resource. Appendix and color version of selected figures can be found at www.wiley.com/go/liu/packaging
Download or read book Continuum and Atomistic Models of Surface Elasticity and Applications written by Lixin Hu and published by . This book was released on 2015 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an analysis of surface elasticity from the Born-Oppenheimer approximation for monatomic crystals. The analysis shows that the relaxations of crystal planes parallel to a free surface can be sufficiently determined by a low-rank algebraic Riccati equation instead of a full-scale molecular dynamic (MD) simulation, and gives new restrictions on physically reasonable atomistic models and simple criteria for surface reconstructions. In the case of surface relaxations, we calculate surface elasticity properties from atomistic models, which are compared with experimental data and prior simulation results. This fundamental research is useful in a variety of applications. First, with the help of the proposed algorithm we quickly calculate the surface tension and determine the equilibrium shape of crystals. Secondly, in previous studies of wave propagation the impact of surface elasticity was not noticed. We find that when the surface/interface gains its own elasticity, the inhomogeneities between the bulk and the surface/interface result in nonlinearity for both interfacial and bulk wave propagation aspects. We study the interfacial wave between two half-spaces with surface elasticity taken into account. ii A sufficient condition for the existence and uniqueness of a subsonic interfacial wave is obtained for general anisotropic materials. In addition, from explicitly calculated dispersion relations of interfacial waves for interfaces between two solids and solid & fluid, we observe that the dispersion relations of interfacial waves are nonlinear at the presence of surface elasticity and depend on surface elasticity parameters. Further, we analyze the wave reflection and refraction with surface elasticity. We find that both the amplitude ratios and energy rates of reflected and refracted waves become dependent on the incident wave frequency. Also, the analysis of the existence of reflected and refracted waves shows that when the incident angle is above some critical angle, the corresponding reflected or refracted waves become typical interfacial waves. Finally, from Landau phenomenological theory we propose a model for size dependence of phase transformation temperature of ferroelectric nano-particles. We postulate that the surface effect plays an important role of such size effect. Our model shows the size dependence and predicts the critical size for certain ferroelectric particles.
Download or read book Continuum Mechanics and Thermodynamics written by Ellad B. Tadmor and published by Cambridge University Press. This book was released on 2012 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats subjects directly related to nonlinear materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.
Download or read book Polymer Science A Comprehensive Reference written by and published by Newnes. This book was released on 2012-12-05 with total page 7752 pages. Available in PDF, EPUB and Kindle. Book excerpt: The progress in polymer science is revealed in the chapters of Polymer Science: A Comprehensive Reference, Ten Volume Set. In Volume 1, this is reflected in the improved understanding of the properties of polymers in solution, in bulk and in confined situations such as in thin films. Volume 2 addresses new characterization techniques, such as high resolution optical microscopy, scanning probe microscopy and other procedures for surface and interface characterization. Volume 3 presents the great progress achieved in precise synthetic polymerization techniques for vinyl monomers to control macromolecular architecture: the development of metallocene and post-metallocene catalysis for olefin polymerization, new ionic polymerization procedures, and atom transfer radical polymerization, nitroxide mediated polymerization, and reversible addition-fragmentation chain transfer systems as the most often used controlled/living radical polymerization methods. Volume 4 is devoted to kinetics, mechanisms and applications of ring opening polymerization of heterocyclic monomers and cycloolefins (ROMP), as well as to various less common polymerization techniques. Polycondensation and non-chain polymerizations, including dendrimer synthesis and various "click" procedures, are covered in Volume 5. Volume 6 focuses on several aspects of controlled macromolecular architectures and soft nano-objects including hybrids and bioconjugates. Many of the achievements would have not been possible without new characterization techniques like AFM that allowed direct imaging of single molecules and nano-objects with a precision available only recently. An entirely new aspect in polymer science is based on the combination of bottom-up methods such as polymer synthesis and molecularly programmed self-assembly with top-down structuring such as lithography and surface templating, as presented in Volume 7. It encompasses polymer and nanoparticle assembly in bulk and under confined conditions or influenced by an external field, including thin films, inorganic-organic hybrids, or nanofibers. Volume 8 expands these concepts focusing on applications in advanced technologies, e.g. in electronic industry and centers on combination with top down approach and functional properties like conductivity. Another type of functionality that is of rapidly increasing importance in polymer science is introduced in volume 9. It deals with various aspects of polymers in biology and medicine, including the response of living cells and tissue to the contact with biofunctional particles and surfaces. The last volume is devoted to the scope and potential provided by environmentally benign and green polymers, as well as energy-related polymers. They discuss new technologies needed for a sustainable economy in our world of limited resources. Provides broad and in-depth coverage of all aspects of polymer science from synthesis/polymerization, properties, and characterization methods and techniques to nanostructures, sustainability and energy, and biomedical uses of polymers Provides a definitive source for those entering or researching in this area by integrating the multidisciplinary aspects of the science into one unique, up-to-date reference work Electronic version has complete cross-referencing and multi-media components Volume editors are world experts in their field (including a Nobel Prize winner)
Download or read book Heterogeneous Materials written by Muhammad Sahimi and published by Springer Science & Business Media. This book was released on 2003-05-15 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes and discusses the properties of heterogeneous materials, comparing two fundamental approaches to describing and predicting materials’ properties. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.
Download or read book JSME International Journal written by and published by . This book was released on 1998 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt:
