Practical Multiscaling
Software
Other digital
400 pages
978-1-118-53486-1 (ISBN)
Description
Multiscale computations have been identified as one of the areas critical to future nanotechnology and biotechnology advances. Combining fundamental theory and practical methods of multiscale modeling, Practical Multiscaling contains a detailed exposition of the state-of-the-art multiscale theories and their insertion into conventional (single-scale) finite element code architecture. Presenting fundamental modeling techniques aimed at bridging diverse temporal and spatial scales, the text focuses on practical multiscale methods that account for fine-scale (material) details, but do not require their precise resolution. This is a trove of valuable material for graduate and postgraduate students.
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Content
Preface 1 Chapter 1: Introduction to multiscale methods 1.1 The rationale for multiscale computations 1.2 The hype and the reality 1.3 Examples and qualification of multiscale methods 1.4 Nomenclature and definitions 1.5 Notation 2 Chapter 2: Upscaling/Downscaling of Continua 2.1 Introduction 2.2 Homogenizaton of linear heterogeneous media 2.3 Upscaling based on enhanced kinematics 2.4 Homogenization of nonlinear heterogeneous media 2.5 Higher order homogenization 2.6 Multiple-scale homogenization 2.7 Going beyond upscaling -- homogenization-based multigrid 3 Chapter 3: Upscaling/Downscaling of Atomistic/Continuum Media 3.1 Introduction 3.2 Governing equations 3.3 Generalized mathematical homogenization (GMH) 3.4 Finite element implementation and numerical verification 3.5 Statistical ensemble 3.6 Verification 3.7 Going beyond upscaling 4 Chapter 4: Reduced Order Homogenization 4.1 Introduction 4.2 Reduced order homogenization for two-scale problems 4.3 Lower order approximation of eigenstrains 4.4 Extension to nonlocal heterogeneous media 4.5 Extension to dispersive heterogeneous media 4.6 Extension to multiple spatial scales 4.7 Extension to large deformations 4.8 Extension to multiple temporal scales with application to fatigue 4.9 Extension to multiphysics problems 5 Chapter 5: Scale-separation-free Upscaling/Downscaling of Continua 5.1 Introduction 5.2 Computational continua (C2) 5.3 Reduced order computational continua (RC2) 5.4 Nonlocal quadrature in multidimensions 5.5 Model Verification 6 Chapter 6: Multiscale Design Software 6.1 Introduction 6.2 Microanalysis with MDS-Lite 6.3 Macroanalysis with MDS-Lite