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Author :
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (912 download)
Download or read book Modeling and Analysis of a Phase Field System for Damage and Phase Separation Processes in Solids written by and published by . This book was released on 2013 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christian Heinemann
Publisher : Springer Science & Business Media
ISBN 13 : 365805252X
Total Pages : 177 pages
Book Rating : 4.6/5 (58 download)
Download or read book Phase Separation Coupled with Damage Processes written by Christian Heinemann and published by Springer Science & Business Media. This book was released on 2014-03-24 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors explore a unifying model which couples phase separation and damage processes in a system of partial differential equations. The model has technological applications to solder materials where interactions of both phenomena have been observed and cannot be neglected for a realistic description. The equations are derived in a thermodynamically consistent framework and suitable weak formulations for various types of this coupled system are presented. In the main part, existence of weak solutions is proven and degenerate limits are investigated.
Author : Nikolas Provatas
Publisher : John Wiley & Sons
ISBN 13 : 3527632379
Total Pages : 323 pages
Book Rating : 4.5/5 (276 download)
Download or read book Phase-Field Methods in Materials Science and Engineering written by Nikolas Provatas and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and self-contained, one-stop source discusses phase-field methodology in a fundamental way, explaining advanced numerical techniques for solving phase-field and related continuum-field models. It also presents numerical techniques used to simulate various phenomena in a detailed, step-by-step way, such that readers can carry out their own code developments. Features many examples of how the methods explained can be used in materials science and engineering applications.
Author : Tina R. Hartley
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (246 download)
Download or read book An Analysis of Phase Separation Processes for Stochastic and Nonlocal Extensions of the Classical Phase-field Model written by Tina R. Hartley and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase separation in composite materials, or materials that are made up of two or more different components, is a process in which the material separates over time into regions of predominantly one component or the other. Because these composite materials are often developed to be used under certain conditions, significant changes of this nature in their material composition can dramatically affect their performance, thus it is important to understand the dynamic behavior of these changes. One mathematical model of phase separation is the classical phase field model, which is a system of nonlinear evolution equations that describes nonisothermal phase separation. Instead of a composite material, the phase field model describes pure materials which can assume two different phases; for example, a solid and a liquid phase. In this dissertation, I analyze the behavior of solutions of the phase field model, along with two extensions to the classical model. One extension is the addition of stochastic terms to the model, thus incorporating random behavior into the equations to address fluctuations in temperature, structural imperfections of the material, or other unknown effects. The other extension is the addition of a nonlocal operator to account for long range interactions. The behavior of all three variations of the phase field model is studied through numerical simulations, and the results compared to describe the differences between the models. In addition, I present a proof showing that the numerical method converges to the true solution of the phase field model.
Author : Christian Heinemann
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (959 download)
Download or read book A Temperature-dependent Phase-field Model for Phase Separation and Damage written by Christian Heinemann and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature (cf., e.g., [21, 22]), we encompass in the model thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More in particular, we prove the existence of "entropic weak solutions", resorting to a solvability concept first introduced in [10] in the framework of Fourier-Navier-Stokes systems and then recently employed in [9, 38] for the study of PDE systems for phase transition and damage. Our global-intime existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.
Author : Blaise Bourdin
Publisher : Springer Science & Business Media
ISBN 13 : 1402063954
Total Pages : 173 pages
Book Rating : 4.4/5 (2 download)
Download or read book The Variational Approach to Fracture written by Blaise Bourdin and published by Springer Science & Business Media. This book was released on 2008-04-19 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting original results from both theoretical and numerical viewpoints, this text offers a detailed discussion of the variational approach to brittle fracture. This approach views crack growth as the result of a competition between bulk and surface energy, treating crack evolution from its initiation all the way to the failure of a sample. The authors model crack initiation, crack path, and crack extension for arbitrary geometries and loads.
Author : A. Rushton
Publisher : Springer Science & Business Media
ISBN 13 : 9400950918
Total Pages : 405 pages
Book Rating : 4.4/5 (9 download)
Download or read book Mathematical Models and Design Methods in Solid-Liquid Separation written by A. Rushton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The separation of finely-divided solids from liquids constitutes an important stage in many industrial processes. Separation of mixtures ranging from highly concentrated slurries to slightly turbid liquids must be effected in circumstances where the solids, liquid or both phases may have value. Separations may be achieved by use of a membrane or filter medium which, positioned in the path of a flowing suspension, will allow passage of the fluid whilst retaining solids on the surface or within the medium. Alternatively the two phases may be separated by sedimentation processes involving gravitational or centrifugal force. In either mode, separation difficulties are sometimes experienced with the result that solid-liquid separation is often a bottleneck in commercial plants. Operational difficulties and plant failures are associated with the random nature of the particles being separated; variations in size, shape, states of aggregation, compressibility, etc. , produce a wide range of problems. Plugging of the filter medium or the collapse of the solids under applied stress lead to slow flowrates of liquid. The colloidal nature of some precipitates makes separation by settling virtually impossible without the use of chemical agents to enhance the size of basic units and to reduce repulsive surface forces. Unit operations such as filtration, comminution, etc. , involve a seemingly bewildering array of machines which makes plant selection a difficult step and reflects the uncer tainties attaching to operations involving the solid )hase. Many types of pressure, vacuum and centrifugal filter are available.
Author : Carlile Lavor
Publisher : Springer
ISBN 13 : 3319940155
Total Pages : 408 pages
Book Rating : 4.3/5 (199 download)
Download or read book Advances in Mathematics and Applications written by Carlile Lavor and published by Springer. This book was released on 2018-09-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.
Author : Andrea Braides
Publisher : Springer Science & Business Media
ISBN 13 : 9783540647713
Total Pages : 176 pages
Book Rating : 4.6/5 (477 download)
Download or read book Approximation of Free-Discontinuity Problems written by Andrea Braides and published by Springer Science & Business Media. This book was released on 1998-09-17 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.
Author : S. Bulent Biner
Publisher : Springer
ISBN 13 : 3319411969
Total Pages : 411 pages
Book Rating : 4.3/5 (194 download)
Download or read book Programming Phase-Field Modeling written by S. Bulent Biner and published by Springer. This book was released on 2017-01-25 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a fast-track pathway to numerical implementation of phase-field modeling—a relatively new paradigm that has become the method of choice for modeling and simulation of microstructure evolution in materials. It serves as a cookbook for the phase-field method by presenting a collection of codes that act as foundations and templates for developing other models with more complexity. Programming Phase-Field Modeling uses the Matlab/Octave programming package, simpler and more compact than other high-level programming languages, providing ease of use to the widest audience. Particular attention is devoted to the computational efficiency and clarity during development of the codes, which allows the reader to easily make the connection between the mathematical formulism and the numerical implementation of phase-field models. The background materials provided in each case study also provide a forum for undergraduate level modeling-simulations courses as part of their curriculum.
Author : Alain Miranville
Publisher : SIAM
ISBN 13 : 1611975921
Total Pages : 216 pages
Book Rating : 4.6/5 (119 download)
Download or read book The Cahn–Hilliard Equation: Recent Advances and Applications written by Alain Miranville and published by SIAM. This book was released on 2019-09-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
Author : Michel Fremond
Publisher : Springer Science & Business Media
ISBN 13 : 9783540665007
Total Pages : 502 pages
Book Rating : 4.6/5 (65 download)
Download or read book Non-Smooth Thermomechanics written by Michel Fremond and published by Springer Science & Business Media. This book was released on 2001-10-09 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on practical problems in mechanical engineering, here the author develops the fundamental concepts of non-smooth mechanics and introduces the necessary background material needed to deal with mechanics involving discontinuities and non-smooth constraints.
Author : Timon Rabczuk
Publisher : MDPI
ISBN 13 : 3039216864
Total Pages : 406 pages
Book Rating : 4.0/5 (392 download)
Download or read book Computational Methods for Fracture written by Timon Rabczuk and published by MDPI. This book was released on 2019-10-28 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a collection of 17 scientific papers about the computational modeling of fracture. Some of the manuscripts propose new computational methods and/or how to improve existing cutting edge methods for fracture. These contributions can be classified into two categories: 1. Methods which treat the crack as strong discontinuity such as peridynamics, scaled boundary elements or specific versions of the smoothed finite element methods applied to fracture and 2. Continuous approaches to fracture based on, for instance, phase field models or continuum damage mechanics. On the other hand, the book also offers a wide range of applications where state-of-the-art techniques are employed to solve challenging engineering problems such as fractures in rock, glass, concrete. Also, larger systems such as fracture in subway stations due to fire, arch dams, or concrete decks are studied.
Author : Pierluigi Colli
Publisher : World Scientific
ISBN 13 : 9812774297
Total Pages : 321 pages
Book Rating : 4.8/5 (127 download)
Download or read book Dissipative Phase Transitions written by Pierluigi Colli and published by World Scientific. This book was released on 2006 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects. Contents: Mathematical Models Including a Hysteresis Operator (T Aiki); Modelling Phase Transitions via an Entropy Equation: Long-Time Behavior of the Solutions (E Bonetti); Global Solution to a One Dimensional Phase Transition Model with Strong Dissipation (G Bonfanti & F Luterotti); A Global in Time Result for an Integro-Differential Parabolic Inverse Problem in the Space of Bounded Functions (F Colombo et al.); Weak Solutions for Stefan Problems with Convections (T Fukao); Memory Relaxation of the One-Dimensional CahnOCoHilliard Equation (S Gatti et al.); Mathematical Models for Phase Transition in Materials with Thermal Memory (G Gentili & C Giorgi); Hysteresis in a First Order Hyperbolic Equation (J Kopfovi); Approximation of Inverse Problems Related to Parabolic Integro-Differential Systems of Caginalp Type (A Lorenzi & E Rocca); Gradient Flow Reaction/Diffusion Models in Phase Transitions (J Norbury & C Girardet); New Existence Result for a 3-D Shape Memory Model (I Pawlow & W M Zajaczkowski); Analysis of a 1-D Thermoviscoelastic Model with Temperature-Dependent Viscosity (R Peyroux & U Stefanelli); Global Attractor for the Weak Solutions of a Class of Viscous Cahn-Hilliard Equations (R Rossi); Stability for Phase Field Systems Involving Indefinite Surface Tension Coefficients (K Shirakawa); Geometric Features of p -Laplace Phase Transitions (E Valdinoci). Readership: Applied mathematicians and researchers in analysis and differential equations."
Author : Jean Lemaitre
Publisher : Springer Science & Business Media
ISBN 13 : 3540272933
Total Pages : 396 pages
Book Rating : 4.5/5 (42 download)
Download or read book Engineering Damage Mechanics written by Jean Lemaitre and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflecting his major contributions to the field, Jean Lemaitre’s "Engineering Damage Mechanics" presents simplified and advanced methods organized within a unified framework for designers of any mechanical component. Explains how to apply continuous damage mechanics to failures of mechanical and civil engineering components in ductile, creep, fatigue and brittle conditions. Incorporates many basic examples, while emphasizing key practical considerations such as material parameter identification, and provides perspective on the advantage and disadvantages of various approaches.
Author : Adora Miracle Padilla
Publisher :
ISBN 13 :
Total Pages : 458 pages
Book Rating : 4.:/5 (56 download)
Download or read book Phase Separation in Freeze-dried Amorphous Solids written by Adora Miracle Padilla and published by . This book was released on 2009 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Morton Gurtin
Publisher : Elsevier
ISBN 13 : 0323159729
Total Pages : 228 pages
Book Rating : 4.3/5 (231 download)
Download or read book Phase Transformations and Material Instabilities in Solids written by Morton Gurtin and published by Elsevier. This book was released on 2012-12-02 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase Transformations and Material Instabilities in Solids contains the proceedings of an interdisciplinary conference on phase transitions and material instabilities in solids, conducted by the Mathematics Research Center of the University of Wisconsin-Madison on October 11-13, 1983 in Madison, Wisconsin. The papers explore phase transformations and material instabilities in solids and cover topics ranging from equilibrium shapes of surfaces to morphological instabilities and dendrite formation. Shock-induced phase transitions are also considered. Comprised of 11 chapters, this book begins with a discussion on material instabilities and the calculus of variations, followed by an analysis of mechanical analogs of coexistent phases. A model for the formation of shear bands in simple shear that involves the description of irreversible mechanical shear and the resulting heat release is then presented. Subsequent chapters focus on the Cauchy and Born hypotheses for crystals; the arrangement of coherent phases in a loaded body; one-dimensional shock layers in Korteweg fluids; and dynamics of first-order phase transitions. The final chapter deals with equilibrium shapes of surfaces and grain boundaries. This monograph will be of interest to students, practitioners, and researchers in mathematics and statistical physics.
