Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Fractals in elastic-hardening plastic materials

J. Li and M. Ostoja-Starzewski
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 466, No. 2114 (8 February 2010), pp. 603-621
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/25661456
Page Count: 19
  • Read Online (Free)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Fractals in elastic-hardening plastic materials
Preview not available

Abstract

Plastic grains are found to form fractal patterns in elastic-hardening plastic materials in two dimensions, made of locally isotropic grains with random fluctuations in plastic limits or elastic/plastic moduli. The spatial assignment of randomness follows a strict-white-noise random field on a square lattice aggregate of square-shaped grains, whereby the flow rule of each grain follows associated plasticity. Square-shaped domains (comprising 256 × 256 grains) are loaded through either one of three macroscopically uniform boundary conditions admitted by the Hill—Mandel condition. Following an evolution of a set of grains that have become plastic, we find that it is monotonically plane filling with an increasing macroscopic load. The set's fractal dimension increases from 0 to 2, with the response under kinematic loading being stiffer than that under mixed-orthogonal loading, which, in turn, is stiffer than the traction controlled one. All these responses display smooth transitions but, as the randomness decreases to zero, they turn into the sharp response of an idealized homogeneous material. The randomness in yield limits has a stronger effect than that in elastic/plastic moduli. On the practical side, the curves of fractal dimension versus applied stress—which indeed display a universal character for a range of different materials—offer a simple method of assessing the inelastic state of the material. A qualitative explanation of the morphogenesis of fractal patterns is given from the standpoint of a correlated percolation on a Markov field on a graph network of grains.

Page Thumbnails

  • Thumbnail: Page 
603
    603
  • Thumbnail: Page 
604
    604
  • Thumbnail: Page 
605
    605
  • Thumbnail: Page 
606
    606
  • Thumbnail: Page 
607
    607
  • Thumbnail: Page 
608
    608
  • Thumbnail: Page 
609
    609
  • Thumbnail: Page 
610
    610
  • Thumbnail: Page 
611
    611
  • Thumbnail: Page 
612
    612
  • Thumbnail: Page 
613
    613
  • Thumbnail: Page 
614
    614
  • Thumbnail: Page 
615
    615
  • Thumbnail: Page 
616
    616
  • Thumbnail: Page 
617
    617
  • Thumbnail: Page 
618
    618
  • Thumbnail: Page 
619
    619
  • Thumbnail: Page 
620
    620
  • Thumbnail: Page 
621
    621