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    Softening Instability: Part I—Localization Into a Planar Band

    Source: Journal of Applied Mechanics:;1988:;volume( 055 ):;issue: 003::page 517
    Author:
    Zdeněk P. Bažant
    DOI: 10.1115/1.3125823
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Distributed damage such as cracking in heterogeneous brittle materials may be approximately described by a strain-softening continuum. To make analytical solutions feasible, the continuum is assumed to be local but localization of softening strain into a region of vanishing volume is precluded by requiring that the softening region, assumed to be in a state of homogeneous strain, must have a certain minimum thickness which is a material property. Exact conditions of stability of an initially uniform strain field against strain localization are obtained for the case of an infinite layer in which the strain localizes into an infinite planar band. First, the problem is solved for small strain. Then a linearized incremental solution is obtained taking into account geometrical nonlinearity of strain. The stability condition is shown to depend on the ratio of the layer thickness to the softening band thickness. It is found that if this ratio is not too large compared to 1, the state of homogeneous strain may be stable well into the softening range. Part II of this study applies Eshelby’s theorem to determine the conditions of localization into ellipsoidal regions in infinite space, and also solves localization into circular or spherical regions in finite bodies.
    keyword(s): Theorems (Mathematics) , Stability , Brittleness , Materials properties , Fracture (Process) AND Thickness ,
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      Softening Instability: Part I—Localization Into a Planar Band

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    http://yetl.yabesh.ir/yetl1/handle/yetl/103474
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    contributor authorZdeněk P. Bažant
    date accessioned2017-05-08T23:26:28Z
    date available2017-05-08T23:26:28Z
    date copyrightSeptember, 1988
    date issued1988
    identifier issn0021-8936
    identifier otherJAMCAV-26297#517_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/103474
    description abstractDistributed damage such as cracking in heterogeneous brittle materials may be approximately described by a strain-softening continuum. To make analytical solutions feasible, the continuum is assumed to be local but localization of softening strain into a region of vanishing volume is precluded by requiring that the softening region, assumed to be in a state of homogeneous strain, must have a certain minimum thickness which is a material property. Exact conditions of stability of an initially uniform strain field against strain localization are obtained for the case of an infinite layer in which the strain localizes into an infinite planar band. First, the problem is solved for small strain. Then a linearized incremental solution is obtained taking into account geometrical nonlinearity of strain. The stability condition is shown to depend on the ratio of the layer thickness to the softening band thickness. It is found that if this ratio is not too large compared to 1, the state of homogeneous strain may be stable well into the softening range. Part II of this study applies Eshelby’s theorem to determine the conditions of localization into ellipsoidal regions in infinite space, and also solves localization into circular or spherical regions in finite bodies.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleSoftening Instability: Part I—Localization Into a Planar Band
    typeJournal Paper
    journal volume55
    journal issue3
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.3125823
    journal fristpage517
    journal lastpage522
    identifier eissn1528-9036
    keywordsTheorems (Mathematics)
    keywordsStability
    keywordsBrittleness
    keywordsMaterials properties
    keywordsFracture (Process) AND Thickness
    treeJournal of Applied Mechanics:;1988:;volume( 055 ):;issue: 003
    contenttypeFulltext
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