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A Temperature Dependent Phase Field Model For Phase Separation And Damage
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Book Synopsis A Temperature-dependent Phase-field Model for Phase Separation and Damage by : Christian Heinemann
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.
Book Synopsis Phase Separation Coupled with Damage Processes by : Christian Heinemann
Download or read book Phase Separation Coupled with Damage Processes written by Christian Heinemann and published by . This book was released on 2014-04-30 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling and Analysis of a Phase Field System for Damage and Phase Separation Processes in Solids by :
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:
Book Synopsis Nonlocal Temperature Dependent Phase Field Models for Non-isothermal Phase Transitions by : Pavel Krejčí
Download or read book Nonlocal Temperature Dependent Phase Field Models for Non-isothermal Phase Transitions written by Pavel Krejčí and published by . This book was released on 2005 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dissipative Phase Transitions by : Pierluigi Colli
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."
Book Synopsis Approximation of Free-Discontinuity Problems by : Andrea Braides
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.
Book Synopsis Phase Separation Coupled with Damage Processes by : Christian Heinemann
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.
Book Synopsis Phase-Field Methods in Materials Science and Engineering by : Nikolas Provatas
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.
Book Synopsis Programming Phase-Field Modeling by : S. Bulent Biner
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.
Book Synopsis An Analysis of Phase Separation Processes for Stochastic and Nonlocal Extensions of the Classical Phase-field Model by : Tina R. Hartley
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.
Book Synopsis Engineering Damage Mechanics by : Jean Lemaitre
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.
Book Synopsis Computational Methods for Fracture by : Timon Rabczuk
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.
Book Synopsis The Variational Approach to Fracture by : Blaise Bourdin
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.
Book Synopsis Phase Field Modeling for Temperature- and Stress-induced Martensitic Phase Transformation by : Gangpeng Wu
Download or read book Phase Field Modeling for Temperature- and Stress-induced Martensitic Phase Transformation written by Gangpeng Wu and published by . This book was released on 2019 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Crystal Plasticity Finite Element Methods by : Franz Roters
Download or read book Crystal Plasticity Finite Element Methods written by Franz Roters and published by John Wiley & Sons. This book was released on 2011-08-04 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.
Book Synopsis Phase Equilibria, Phase Diagrams and Phase Transformations by : Mats Hillert
Download or read book Phase Equilibria, Phase Diagrams and Phase Transformations written by Mats Hillert and published by Cambridge University Press. This book was released on 2007-11-22 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational tools allow material scientists to model and analyze increasingly complicated systems to appreciate material behavior. Accurate use and interpretation however, requires a strong understanding of the thermodynamic principles that underpin phase equilibrium, transformation and state. This fully revised and updated edition covers the fundamentals of thermodynamics, with a view to modern computer applications. The theoretical basis of chemical equilibria and chemical changes is covered with an emphasis on the properties of phase diagrams. Starting with the basic principles, discussion moves to systems involving multiple phases. New chapters cover irreversible thermodynamics, extremum principles, and the thermodynamics of surfaces and interfaces. Theoretical descriptions of equilibrium conditions, the state of systems at equilibrium and the changes as equilibrium is reached, are all demonstrated graphically. With illustrative examples - many computer calculated - and worked examples, this textbook is an valuable resource for advanced undergraduates and graduate students in materials science and engineering.
Book Synopsis The Physics of Phase Transitions by : Pierre Papon
Download or read book The Physics of Phase Transitions written by Pierre Papon and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Physics of Phase Transitions occupies an important place at the crossroads of several fields central to materials sciences. This second edition incorporates new developments in the states of matter physics, in particular in the domain of nanomaterials and atomic Bose-Einstein condensates where progress is accelerating. New information and application examples are included. This work deals with all classes of phase transitions in fluids and solids, containing chapters on evaporation, melting, solidification, magnetic transitions, critical phenomena, superconductivity, and more. End-of-chapter problems and complete answers are included.
