Yvonnet, Julien.
Computational Homogenization of Heterogeneous Materials with Finite Elements [electronic resource] / by Julien Yvonnet. - 1st ed. 2019. - XVI, 221 p. 103 illus., 74 illus. in color. online resource. - Solid Mechanics and Its Applications, 258 2214-7764 ; . - Solid Mechanics and Its Applications, 258 .
Foreword -- Preface -- Introduction -- Review of classical FEM formulations and discretizations -- Conduction properties -- Elasticity and thermoelasticity -- Piezoelectricity -- Porous media -- Second-order linear homogenization -- Filter-based homogenization -- Nonlinear Computational Homogenization -- Bibliography -- Appendices -- Index.
This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.
9783030183837
10.1007/978-3-030-18383-7 doi
Mathematics—Data processing.
Mechanics, Applied.
Solids.
Materials science.
Mathematical physics.
Materials.
Computational Science and Engineering.
Solid Mechanics.
Materials Science.
Theoretical, Mathematical and Computational Physics.
Materials Engineering.
QA71-90
003.3
Computational Homogenization of Heterogeneous Materials with Finite Elements [electronic resource] / by Julien Yvonnet. - 1st ed. 2019. - XVI, 221 p. 103 illus., 74 illus. in color. online resource. - Solid Mechanics and Its Applications, 258 2214-7764 ; . - Solid Mechanics and Its Applications, 258 .
Foreword -- Preface -- Introduction -- Review of classical FEM formulations and discretizations -- Conduction properties -- Elasticity and thermoelasticity -- Piezoelectricity -- Porous media -- Second-order linear homogenization -- Filter-based homogenization -- Nonlinear Computational Homogenization -- Bibliography -- Appendices -- Index.
This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.
9783030183837
10.1007/978-3-030-18383-7 doi
Mathematics—Data processing.
Mechanics, Applied.
Solids.
Materials science.
Mathematical physics.
Materials.
Computational Science and Engineering.
Solid Mechanics.
Materials Science.
Theoretical, Mathematical and Computational Physics.
Materials Engineering.
QA71-90
003.3