Using damage delocalization to model localization phenomena in Bammann-Chiesa-Johnson Metals

Koffi Enakoutsa, Fazle R. Ahad, Kiran Solanki, Yustianto Tjiptowidjojo, Douglas J. Bammann

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The Bammann, Chiesa, and Johnson (BCJ) material model predicts unlimited localization of strain and damage, resulting in a zero dissipation energy at failure. This difficulty resolves when the BCJ model is modified to incorporate a nonlocal evolution equation for the damage, as proposed by Pijaudier-Cabot and Bazant (1987, Nonlocal Damage Theory, ASCE J. Eng. Mech., 113, pp. 1512-1533.). In this work, we theoretically assess the ability of such a modified BCJ model to prevent unlimited localization of strain and damage. To that end, we investigate two localization problems in nonlocal BCJ metals: appearance of a spatial discontinuity of the velocity gradient in any finite, inhomogeneous body, and localization of the dissipation energy into finite bands. We show that in spite of the softening arising from the damage, no spatial discontinuity occurs in the velocity gradient. Also, we find that the dissipation energy is continuously distributed in nonlocal BCJ metals and therefore cannot localize into zones of vanishing volume. As a result, the appearance of any vanishing width adiabatic shear band is impossible in a nonlocal BCJ metal. Finally, we study the finite element (FE) solution of shear banding in a rectangular plate, deformed in plane strain tension and containing an imperfection, thereby illustrating the effects of imperfections and finite size on the localization of strain and damage.

Original languageEnglish (US)
Article number41014
JournalJournal of Engineering Materials and Technology
Issue number4
StatePublished - 2012

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Using damage delocalization to model localization phenomena in Bammann-Chiesa-Johnson Metals'. Together they form a unique fingerprint.

Cite this