On the dilatational wave motion in anisotropic fractal solids

Hady Joumaa and Martin Ostoja-Starzewski

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 127, issue C, 114-130

Abstract: This paper reports a study of wave motion in a generally anisotropic fractal medium (i.e. with different fractal dimensions in different directions), whose constitutive response is represented by an isotropic Hooke's law. First, the governing elastodynamic laws are formulated on the basis of dimensional regularization. It is discovered that the satisfaction of the angular momentum equation precludes the implementation of the classical elasticity theory which results in symmetry of the Cauchy stress tensor. Nevertheless, the classical elastic constitutive model can still be applied to explore dilatational wave propagation; in such a case, the angular momentum balance is “trivially” satisfied. The resulting problem, of eigenvalue type, is solved analytically. A computational finite element method solver is also developed to simulate the problem in its one-dimensional (1d) 1D form, it is validated by the reference solutions generated through the modal analysis. A 3D finite-difference-based solver is also developed and the obtained results match those of the 1D simulation.

Keywords: Elastodynamics; Fractal solid; Dilatational wave (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475413000876
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:127:y:2016:i:c:p:114-130

DOI: 10.1016/j.matcom.2013.03.012

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().