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    The Effect of Rate Dependence on Localization of Deformation and Failure in Softening Solids

    Source: Journal of Applied Mechanics:;2015:;volume( 082 ):;issue: 002::page 21002
    Author:
    Needleman, Alan
    DOI: 10.1115/1.4029180
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: 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 quasistatic 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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      The Effect of Rate Dependence on Localization of Deformation and Failure in Softening Solids

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    contributor authorNeedleman, Alan
    date accessioned2017-05-09T01:14:32Z
    date available2017-05-09T01:14:32Z
    date issued2015
    identifier issn0021-8936
    identifier otherjam_082_02_021002.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/156906
    description abstractLocalization 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 quasistatic 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.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleThe Effect of Rate Dependence on Localization of Deformation and Failure in Softening Solids
    typeJournal Paper
    journal volume82
    journal issue2
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.4029180
    journal fristpage21002
    journal lastpage21002
    identifier eissn1528-9036
    treeJournal of Applied Mechanics:;2015:;volume( 082 ):;issue: 002
    contenttypeFulltext
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