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Practical multiscaling

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"Practical Multiscaling covers fundamental modelling techniques aimed at bridging diverse temporal and spatial scales ranging from the atomic level to a full-scale product level. It focuses on practical multiscale methods that account for fine-scale (material) details but do not require their p...

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Bibliographic Details
Main Author: Fish, J. (Jacob)
Corporate Author: ebrary, Inc
Format: Electronic eBook
Language:English
Published: Chichester, West Sussex, U.K. : John Wiley & Sons Inc., 2014.
Subjects:
Mechanical engineering > Mathematical models.
Continuum mechanics > Mathematical models.
Materials > Mathematical models.
Multiscale modeling.
Scaling laws (Statistical physics)
Mechanical engineering > Computer simulation.
Continuum mechanics > Computer simulation.
Materials > Computer simulation.
Electronic books.
Online Access:An electronic book accessible through the World Wide Web; click to view
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Table of Contents:
  • Chapter 1. Introduction to multiscale methods
  • The rationale for multiscale computations
  • The hype and the reality
  • Examples and qualification of multiscale methods
  • Nomenclature and definitions
  • Notation
  • Chapter 2. Upscaling/Downscaling of Continua
  • Homogenizaton of linear heterogeneous media
  • Upscaling based on enhanced kinematics
  • Homogenization of nonlinear heterogeneous media
  • Higher order homogenization
  • Multiple-scale homogenization
  • Going beyond upscaling : homogenization-based multigrid
  • Chapter 3. Upscaling/Downscaling of Atomistic/Continuum Media
  • Governing equations
  • Generalized mathematical homogenization (GMH)
  • Finite element implementation and numerical verification
  • Statistical ensemble
  • Verification
  • Going beyond upscaling
  • Chapter 4. Reduced Order Homogenization
  • Reduced order homogenization for two-scale problems
  • Lower order approximation of eigenstrains
  • Extension to nonlocal heterogeneous media
  • Extension to dispersive heterogeneous media
  • Extension to multiple spatial scales
  • Extension to large deformations
  • Extension to multiple temporal scales with application to fatigue
  • Extension to multiphysics problems
  • Chapter 5. Scale-separation-free Upscaling/Downscaling of Continua
  • Computational continua (C2)
  • Reduced order computational continua (RC2)
  • Nonlocal quadrature in multidimensions
  • Model Verification
  • Chapter 6. Multiscale Design Software
  • Microanalysis with MDS-Lite
  • Macroanalysis with MDS-Lite.

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