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Erschienen in:

2019 | OriginalPaper | Buchkapitel

25. Continuum Homogenization of Fractal Media

verfasst von : Martin Ostoja-Starzewski, Jun Li, Paul N. Demmie

Erschienen in: Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Verlag: Springer International Publishing

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Abstract

This chapter reviews the modeling of fractal materials by homogenized continuum mechanics using calculus in non-integer dimensional spaces. The approach relies on expressing the global balance laws in terms of fractional integrals and, then, converting them to integer-order integrals in conventional (Euclidean) space. Via localization, this allows development of local balance laws of fractal media (continuity, linear and angular momenta, energy, and second law) and, in case of elastic responses, formulation of wave equations in several settings (1D and 3D wave motions, fractal Timoshenko beam, and elastodynamics under finite strains). Next, follows an account of extremum and variational principles, and fracture mechanics. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions and reduce to conventional forms for continuous media with Euclidean geometries upon setting the dimensions to integers.

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Titel: Continuum Homogenization of Fractal Media
verfasst von: Martin Ostoja-Starzewski
Jun Li
Paul N. Demmie
Verlag: Springer International Publishing
Buch: Handbook of Nonlocal Continuum Mechanics for Materials and Structures
Print ISBN: 978-3-319-58727-1

Electronic ISBN: 978-3-319-58729-5

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-319-58729-5_18

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