Multiphysics Phase Field Fracture
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Multiphysics Phase Field Fracture
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Author : Thomas Wick
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-12
Multiphysics Phase Field Fracture written by Thomas Wick and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-12 with Mathematics categories.
This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance between scientific computing aspects and numerical modeling of nonstationary coupled variational inequality systems. Therein, a focus is on nonlinear solvers, goal-oriented error estimation, predictor-corrector adaptivity, and interface conditions. Engineering applications show the potential for tackling practical problems within the fields of solid mechanics, porous media, and fluidstructure interaction.
Multiphysics Phase Field Fracture
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Author : Thomas Wick
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-12
Multiphysics Phase Field Fracture written by Thomas Wick and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-12 with Mathematics categories.
This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance between scientific computing aspects and numerical modeling of nonstationary coupled variational inequality systems. Therein, a focus is on nonlinear solvers, goal-oriented error estimation, predictor-corrector adaptivity, and interface conditions. Engineering applications show the potential for tackling practical problems within the fields of solid mechanics, porous media, and fluidstructure interaction.
Approximation Of Free Discontinuity Problems
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Author : Andrea Braides
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-17
Approximation Of Free Discontinuity Problems written by Andrea Braides and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-17 with Mathematics categories.
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.
Computational Methods Of Multi Physics Problems
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Author : Timon Rabczuk
language : en
Publisher: MDPI
Release Date : 2019-08-20
Computational Methods Of Multi Physics Problems written by Timon Rabczuk and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-20 with Technology & Engineering categories.
This book offers a collection of six papers addressing problems associated with the computational modeling of multi-field problems. Some of the proposed contributions present novel computational techniques, while other topics focus on applying state-of-the-art techniques in order to solve coupled problems in various areas including the prediction of material failure during the lithiation process, which is of major importance in batteries; efficient models for flexoelectricity, which require higher-order continuity; the prediction of composite pipes under thermomechanical conditions; material failure in rock; and computational materials design. The latter exploits nano-scale modeling in order to predict various material properties for two-dimensional materials with applications in, for example, semiconductors. In summary, this book provides a good overview of the computational modeling of different multi-field problems.
Programming Phase Field Modeling
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Author : S. Bulent Biner
language : en
Publisher: Springer
Release Date : 2017-01-25
Programming Phase Field Modeling written by S. Bulent Biner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-25 with Technology & Engineering categories.
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.
Multiscale Modeling Of Curing And Crack Propagation In Fiber Reinforced Thermosets
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Author : Schöller, Lukas
language : en
Publisher: KIT Scientific Publishing
Release Date : 2024-03-15
Multiscale Modeling Of Curing And Crack Propagation In Fiber Reinforced Thermosets written by Schöller, Lukas and has been published by KIT Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-15 with categories.
During the production of fiber-reinforced thermosets, the resin material undergoes a reaction that can lead to damage. A two-stage polymerization reaction is modeled using molecular dynamics and evaluations of the system including a fiber surface are performed. In addition, a phase-field model for crack propagation in heterogeneous systems is derived. This model is able to predict crack growth where established models fail. Finally, the model is used to predict crack formation during curing.
A Primer On Mathematical Modelling
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Author : Alfio Quarteroni
language : en
Publisher: Springer Nature
Release Date : 2020-10-09
A Primer On Mathematical Modelling written by Alfio Quarteroni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-09 with Mathematics categories.
In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.
Moving Boundary Problems In Multi Physics Coupling Processes
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Author : Leilei Chen
language : en
Publisher: Frontiers Media SA
Release Date : 2023-07-19
Moving Boundary Problems In Multi Physics Coupling Processes written by Leilei Chen and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-19 with Science categories.
Newton Methods For Nonlinear Problems
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Author : Peter Deuflhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-13
Newton Methods For Nonlinear Problems written by Peter Deuflhard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-13 with Mathematics categories.
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.
Theory Of Porous Media
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Author : Reint de Boer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Porous Media written by Reint de Boer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Porous media theories play an important role in many branches of engineering, including material science, the petroleum industry, chemical engineering, and soil mechanics, as well as biomechanics. This book offers a consistent treatment of the material-independent fundamental equations of the theory of porous media, formulates constitutive equations for frictional materials in the elastic and plastic range, and traces the historical development of porous media theory. Thus, for the first time, a unique treatment of fluid-saturated porous solids is presented. The corresponding theory is explained by its historical progression, and its current state is thoroughly described.