Homogenization Methods For Multiscale Mechanics
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Homogenization Methods For Multiscale Mechanics
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Author : Chiang C. Mei
language : en
Publisher: World Scientific
Release Date : 2010
Homogenization Methods For Multiscale Mechanics written by Chiang C. Mei and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
In many physical problems several scales present either in space or in time, caused by either inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first construct micro-scale models, and then deduce the macro-scale laws and the constitutive relations by properly averaging over the micro-scale. The perturbation method of multiple scales can be used to derive averaged equations for a much larger scale from considerations of the small scales. In the mechanics of multiscale media, the analytical scheme of upscaling is known as the Theory of Homogenization The authors share the view that the general methods of homogenization should be more widely understood and practiced by applied scientists and engineers. Hence this book is aimed at providing a less abstract treatment of the theory of homogenization for treating inhomogeneous media, and at illustrating its broad range of applications. Each chapter deals with a different class of physical problems. To tackle a new problem, the novel approach of first discussing the physically relevant scales, then identifying the small parameters and their roles in the normalized governing equations is adopted. The details of asymptotic analysis are only explained afterwards.
Homogenization Methods For Multiscale Mechanics
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Author : Chiang C Mei
language : en
Publisher: World Scientific
Release Date : 2010-09-23
Homogenization Methods For Multiscale Mechanics written by Chiang C Mei and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-23 with Mathematics categories.
In many physical problems several scales are present in space or time, caused by inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first construct micro-scale models, and then deduce the macro-scale laws and the constitutive relations by properly averaging over the micro-scale. The perturbation method of multiple scales can be used to derive averaged equations for a much larger scale from considerations of the small scales. In the mechanics of multiscale media, the analytical scheme of upscaling is known as the Theory of Homogenization.The authors share the view that the general methods of homogenization should be more widely understood and practiced by applied scientists and engineers. Hence this book is aimed at providing a less abstract treatment of the theory of homogenization for treating inhomogeneous media, and at illustrating its broad range of applications. Each chapter deals with a different class of physical problems. To tackle a new problem, the approach of first discussing the physically relevant scales, then identifying the small parameters and their roles in the normalized governing equations is adopted. The details of asymptotic analysis are only explained afterwards.
Multiscale Methods In Computational Mechanics
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Author : René de Borst
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-09
Multiscale Methods In Computational Mechanics written by René de Borst 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 2010-10-09 with Computers categories.
This work gives a modern, up-to-date account of recent developments in computational multiscale mechanics. Both upscaling and concurrent computing methodologies will be addressed for a range of application areas in computational solid and fluid mechanics: Scale transitions in materials, turbulence in fluid-structure interaction problems, multiscale/multilevel optimization, multiscale poromechanics. A Dutch-German research group that consists of qualified and well-known researchers in the field has worked for six years on the topic of computational multiscale mechanics. This text provides a unique opportunity to consolidate and disseminate the knowledge gained in this project. The addition of chapters written by experts outside this working group provides a broad and multifaceted view of this rapidly evolving field.
Computer Methods In Mechanics
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Author : Mieczyslaw Kuczma
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-10
Computer Methods In Mechanics written by Mieczyslaw Kuczma 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 2010-03-10 with Technology & Engineering categories.
Prominent scientists present the latest achievements in computational methods and mechanics in this book. These lectures were held at the CMM 2009 conference.
Encyclopedia Of Computational Mechanics
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Author :
language : en
Publisher:
Release Date : 2007
Encyclopedia Of Computational Mechanics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mechanics, Applied categories.
Multiscale Biomechanics
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Author : Jean-Francois Ganghoffer
language : en
Publisher: Elsevier
Release Date : 2018-02-03
Multiscale Biomechanics written by Jean-Francois Ganghoffer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-03 with Science categories.
Multiscale Biomechanics provides new insights on multiscale static and dynamic behavior of both soft and hard biological tissues, including bone, the intervertebral disk, biological membranes and tendons. The physiological aspects of bones and biological membranes are introduced, along with micromechanical models used to compute mechanical response. A modern account of continuum mechanics of growth and remodeling, generalized continuum models to capture internal lengths scales, and dedicated homogenization methods are provided to help the reader with the necessary theoretical foundations. Topics discussed include multiscale methods for fibrous media based on discrete homogenization, generalized continua constitutive models for bone, and a presentation of recent theoretical and numerical advances. In addition, a refresher on continuum mechanics and more advanced background related to differential geometry, configurational mechanics, mechanics of growth, thermodynamics of open systems and homogenization methods is given in separate chapters. Numerical aspects are treated in detail, and simulations are presented to illustrate models. This book is intended for graduate students and researchers in biomechanics interested in the latest research developments, as well as those who wish to gain insight into the field of biomechanics. - Provides a clear exposition of multiscale methods for fibrous media based on discrete homogenization and the consideration of generalized continua constitutive models for bone - Presents recent theoretical and numerical advances for bone remodeling and growth - Includes the necessary theoretical background that is exposed in a clear and self-contained manner - Covers continuum mechanics and more advanced background related to differential geometry, configurational mechanics, mechanics of growth, thermodynamics of open systems and homogenization methods
Multiscale Modelling Of Plasticity And Fracture By Means Of Dislocation Mechanics
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Author : Peter Gumbsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-30
Multiscale Modelling Of Plasticity And Fracture By Means Of Dislocation Mechanics written by Peter Gumbsch 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 2011-01-30 with Technology & Engineering categories.
The latest state of simulation techniques to model plasticity and fracture in crystalline materials on the nano- and microscale is presented. Discrete dislocation mechanics and the neighbouring fields molecular dynamics and crystal plasticity are central parts. The physical phenomena, the theoretical basics, their mathematical description and the simulation techniques are introduced and important problems from the formation of dislocation structures to fatigue and fracture from the nano- to microscale as well as it’s impact on the macro behaviour are considered.
Multiscale Problems
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Author : Alain Damlamian
language : en
Publisher: World Scientific
Release Date : 2011
Multiscale Problems written by Alain Damlamian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier?Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.
Multiscale Modeling Approaches For Composites
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Author : George Chatzigeorgiou
language : en
Publisher: Elsevier
Release Date : 2022-01-19
Multiscale Modeling Approaches For Composites written by George Chatzigeorgiou and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-19 with Technology & Engineering categories.
Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples. The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then passes to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green's tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory. Key features: Bridges theory and practice, providing step-by-step instructions for implementing multiscale modeling approaches for composites and the theoretical concepts behind them Covers boundary conditions, data-exchange between scales, the Hill-Mandel principle, average stress and strain theorems, and more Discusses how to obtain composite properties using various full-field and mean-field approaches Includes access to a companion site featuring the numerical examples, Python, and ABAQUS codes
Multiscale Modeling In Solid Mechanics
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Author : Ugo Galvanetto
language : en
Publisher: World Scientific
Release Date : 2010
Multiscale Modeling In Solid Mechanics written by Ugo Galvanetto and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Technology & Engineering categories.
This unique volume presents the state of the art in the field of multiscale modeling in solid mechanics, with particular emphasis on computational approaches. For the first time, contributions from both leading experts in the field and younger promising researchers are combined to give a comprehensive description of the recently proposed techniques and the engineering problems tackled using these techniques. The book begins with a detailed introduction to the theories on which different multiscale approaches are based, with regards to linear homogenization as well as various nonlinear approaches. It then presents advanced applications of multiscale approaches applied to nonlinear mechanical problems. Finally, the novel topic of materials with self-similar structure is discussed.