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    Saint-Venant End Effects for Incremental Plane Deformations of Incompressible Nonlinearly Elastic Materials

    Source: Journal of Applied Mechanics:;1985:;volume( 052 ):;issue: 004::page 847
    Author:
    R. Abeyaratne
    ,
    C. O. Horgan
    ,
    D.-T. Chung
    DOI: 10.1115/1.3169157
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This paper is concerned with assessing the extent of Saint-Venant end effects within the theory of small deformations superposed on a large deformation for plane strain of homogeneous, isotropic, incompressible materials. The problem considered is that of plane deformation of a body which in its undeformed configuration, occupies a semi-infinite strip. The long sides of the strip are free of traction while the short side is subjected to prescribed normal and shear tractions. A purely normal tensile traction is applied uniformly at the remote end. For the case of slightly nonuniform end tractions at the near end, it is shown that the resulting stress distribution differs from that of homogeneous uniaxial tension by an exponentially decaying function of the distance from the end of the strip. The decay rate is characterized explicitly in terms of the strip width, the remotely applied tensile load, and constitutive parameters. Numerical results are provided for the Mooney-Rivlin material and power-law materials which either harden or soften in tension.
    keyword(s): Deformation , Strips , Tension , Traction , Stress , Shear (Mechanics) , Stress concentration AND Plane strain ,
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      Saint-Venant End Effects for Incremental Plane Deformations of Incompressible Nonlinearly Elastic Materials

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/99290
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    contributor authorR. Abeyaratne
    contributor authorC. O. Horgan
    contributor authorD.-T. Chung
    date accessioned2017-05-08T23:19:19Z
    date available2017-05-08T23:19:19Z
    date copyrightDecember, 1985
    date issued1985
    identifier issn0021-8936
    identifier otherJAMCAV-26261#847_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/99290
    description abstractThis paper is concerned with assessing the extent of Saint-Venant end effects within the theory of small deformations superposed on a large deformation for plane strain of homogeneous, isotropic, incompressible materials. The problem considered is that of plane deformation of a body which in its undeformed configuration, occupies a semi-infinite strip. The long sides of the strip are free of traction while the short side is subjected to prescribed normal and shear tractions. A purely normal tensile traction is applied uniformly at the remote end. For the case of slightly nonuniform end tractions at the near end, it is shown that the resulting stress distribution differs from that of homogeneous uniaxial tension by an exponentially decaying function of the distance from the end of the strip. The decay rate is characterized explicitly in terms of the strip width, the remotely applied tensile load, and constitutive parameters. Numerical results are provided for the Mooney-Rivlin material and power-law materials which either harden or soften in tension.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleSaint-Venant End Effects for Incremental Plane Deformations of Incompressible Nonlinearly Elastic Materials
    typeJournal Paper
    journal volume52
    journal issue4
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.3169157
    journal fristpage847
    journal lastpage852
    identifier eissn1528-9036
    keywordsDeformation
    keywordsStrips
    keywordsTension
    keywordsTraction
    keywordsStress
    keywordsShear (Mechanics)
    keywordsStress concentration AND Plane strain
    treeJournal of Applied Mechanics:;1985:;volume( 052 ):;issue: 004
    contenttypeFulltext
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