Computational Homogenization of Heterogeneous Materials with Finite Elements. (2019)

• Record Type: Book
• Further Information: Note: Julien Yvonnet.
• Other Names: Yvonnet, Julien
• Contents: Intro; Foreword; Preface; Acknowledgements; Contents; 1 Introduction; 1.1 Why Computational Homogenization?; 1.2 Brief Background and Recent Advances; 1.3 Industrial Applications and Use in Commercial Softwares; 1.4 Position of the Present Monograph as Compared to Available Other Books on That Topic; 1.5 Overview; References; 2 Review of Classical FEM Formulations and Discretizations; 2.1 Steady-State Thermal Problem; 2.1.1 Strong Form of Equations; 2.1.2 Weak Forms of Equations; 2.1.3 2D FEM Discretization with Linear Elements; 2.1.4 Assembly of the Elementary Systems 2.1.5 Prescribing Dirichlet Boundary Conditions2.2 Linear Elasticity; 2.2.1 Strong Form; 2.2.2 Weak Form; 2.2.3 2D Discretization; 2.2.4 Assembly; References; 3 Conduction Properties; 3.1 The Notion of RVE; 3.2 Localization Problem; 3.3 Averaged Quantities and Hill-Mandel Lemma; 3.3.1 Averaging Theorem: Temperature Gradient; 3.3.2 Averaging Theorem: Heat Flux; 3.3.3 Hill-Mandel Lemma; 3.4 Computation of the Effective Conductivity Tensor; 3.4.1 The Superposition Principle; 3.4.2 Definition of the Effective Conductivity Tensor 3.5 Periodic Boundary Conditions for the Thermal Problem: Numerical Implementation3.6 Numerical Calculation of Effective Transverse Conductivity with 2D FEM; 3.7 Numerical Examples; References; 4 Elasticity and Thermoelasticity; 4.1 Localization Problem for Elasticity; 4.2 Averaged Quantities and Hill-Mandel Lemma; 4.2.1 Averaging Theorem: Strain; 4.2.2 Averaging Theorem: Stress; 4.2.3 Hill-Mandel Lemma; 4.3 Definition of the Effective Elastic Tensor; 4.3.1 Strain Approach; 4.3.2 Stress Approach; 4.4 Computations of the Effective Properties with FEM 4.4.1 2D Case: Transverse Effective Properties4.4.2 Computation of Out-of-Plane Elastic Properties Using a 2D RVE; 4.4.3 Full 3D Case; 4.5 Periodic Boundary Conditions for 2D Elastic Problem: Practical Implementation; 4.6 Extension to Thermoelasticity; 4.7 Numerical Examples; 4.8 An Illustrative Example: Calculation of Effective Properties in 3D Printed Lattices; References; 5 Piezoelectricity; 5.1 Linear Piezoelectricity; 5.2 Localization Problem for Piezoelectricity; 5.3 Macroscopic Operators; 5.4 FEM Formulation for 2D Piezoelectricity Taking into Account Out-of-Plane Effects 5.5 Computation of Effective Operators with FEM5.6 Numerical Example; References; 6 Saturated Porous Media; 6.1 Poroelasticity; 6.1.1 Localization Problem; 6.1.2 Effective Poroelastic Behavior and Its FEM Numerical Computation; 6.1.3 Validation Examples; 6.2 Effective Permeability; 6.2.1 Localization Problem; 6.2.2 Definition and Computation of the Effective Permeability; 6.3 Reference Solutions; References; 7 Linear Viscoelastic Materials; 7.1 Linear Viscoelasticity; 7.1.1 1D Formulation; 7.1.2 3D Isotropic Formulation; 7.2 Localization Problem and FEM Procedure for the RVE Problem
• Publisher Details: Cham : Springer
• Publication Date: 2019
• Extent: 1 online resource (231 p.)
• Subjects: 515/.353; 004; Homogenization (Differential equations); Finite element method; Finite element method; Homogenization (Differential equations); Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030183837; 3030183831
• Related ISBNs: 3030183823; 9783030183820
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