TY - JOUR
T1 - Using damage delocalization to model localization phenomena in Bammann-Chiesa-Johnson Metals
AU - Enakoutsa, Koffi
AU - Ahad, Fazle R.
AU - Solanki, Kiran
AU - Tjiptowidjojo, Yustianto
AU - Bammann, Douglas J.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
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U2 - 10.1115/1.4007352
DO - 10.1115/1.4007352
M3 - Article
AN - SCOPUS:84866092262
SN - 0094-4289
VL - 134
JO - Journal of Engineering Materials and Technology
JF - Journal of Engineering Materials and Technology
IS - 4
M1 - 41014
ER -