A localization-induced cohesive model has been proposed for shear band evolution, crack growth, and fracture. Strain gradient theory has been applied to establish the criterion of the onset of localization and the governing equation in the post-bifurcation stage. Analytical solutions in one-dimensional case are used to establish the “traction-separation” law, in which strain gradient and material intrinsic length scale present strong effects. In addition, the solution predicts a finite width for the localization-induced band. It is observed that a larger length scale contributes to the growth of a larger width of localization region and separation for softening materials. The proposed model provides a procedure to establish the fracture toughness analytically since the material length scale is taken into account. From the traction-separation analysis, it is found that damage decreases separation, whereas an increase in material length scale increases the opening displacement; however, the traction-normalized opening displacement curves (with respect to the material length scale) are identical. Based on the methodology of multiple scale analysis in meshfree method, a computational approach has been proposed to enrich the one-dimensional traction-separation law to define fracture. [S0021-8936(00)01104-1]
Localization-Induced Band and Cohesive Model1
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received and accepted by the ASME Applied Mechanics Division, March 7, 2000. Associate Technical Editor: B. M. Moran. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Hao, S., Liu, W. K., and Qian, D. (March 7, 2000). "Localization-Induced Band and Cohesive Model." ASME. J. Appl. Mech. December 2000; 67(4): 803–812. https://doi.org/10.1115/1.1325413
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