Localization of deformation and failure, a complete loss of stress carrying capacity, is studied for two rate dependent constitutive relations: (i) a Kelvin–Voigt solid and (ii) a viscoplastic solid. A planar block infinite in one direction is subjected to monotonically increasing shear displacements at a fixed rate. Geometry changes are neglected and attention is confined to quasi-static loading conditions. For the Kelvin–Voigt solid, localization precedes failure if there is hardening outside the band and softening inside the band while failure precedes localization if there is softening both inside and outside the band. For the viscoplastic solid, localization precedes failure when there is softening inside the band regardless of the sign of the hardening parameter outside band. For the Kelvin–Voigt solid, it is found that the localization time (or strain) varies logarithmically with the band thickness for small values of band thickness while the time (or strain) to a complete loss of stress carrying capacity has, in general, a different scaling with band thickness. For the viscoplastic solid, with plastic dissipation outside the band as well as inside the band, the strain and the total plastic dissipation to failure are nearly independent of band thickness for sufficiently small thickness values, with what is sufficiently small decreasing with decreasing rate sensitivity. Possible implications for grid based modeling of localization and failure are discussed.
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February 2015
Research-Article
The Effect of Rate Dependence on Localization of Deformation and Failure in Softening Solids
Alan Needleman
Alan Needleman
Fellow ASME
Professor
Department of Materials Science
and Engineering,
Professor
Department of Materials Science
and Engineering,
University of North Texas
,Denton, TX 76207
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Alan Needleman
Fellow ASME
Professor
Department of Materials Science
and Engineering,
Professor
Department of Materials Science
and Engineering,
University of North Texas
,Denton, TX 76207
Contributed by the Applied Mechanics of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 17, 2014; final manuscript received November 15, 2014; accepted manuscript posted November 20, 2014; published online December 11, 2014. Editor: Yonggang Huang.
J. Appl. Mech. Feb 2015, 82(2): 021002 (7 pages)
Published Online: February 1, 2015
Article history
Received:
October 17, 2014
Revision Received:
November 15, 2014
Accepted:
November 20, 2014
Online:
December 11, 2014
Citation
Needleman, A. (February 1, 2015). "The Effect of Rate Dependence on Localization of Deformation and Failure in Softening Solids." ASME. J. Appl. Mech. February 2015; 82(2): 021002. https://doi.org/10.1115/1.4029180
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