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    Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate

    Source: Journal of Engineering Materials and Technology:;1998:;volume( 120 ):;issue: 002::page 131
    Author:
    Zdeněk P. Bažant
    DOI: 10.1115/1.2807001
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: It is shown that there exist approximations of the Hencky (logarithmic) finite strain tensor of various degrees of accuracy, having the following characteristics: (1) The tensors are close enough to the Hencky strain tensor for most practical purposes and coincide with it up to the quadratic term of the Taylor series expansion; (2) are easy to compute (the spectral representation being unnecessary); and (3) exhibit tension-compression symmetry (i.e., the strain tensor of the inverse transformation is minus the original strain tensor). Furthermore, an additive decomposition of the proposed strain tensor into volumetric and deviatoric (isochoric) parts is given. The deviatoric part depends on the volume change, but this dependence is negligible for materials that are incapable of large volume changes. A general relationship between the rate of the approximate Hencky strain tensor and the deformation rate tensor can be easily established.
    keyword(s): Tensors , Approximation , Compression , Tension AND Deformation ,
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      Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate

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    http://yetl.yabesh.ir/yetl1/handle/yetl/120529
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    contributor authorZdeněk P. Bažant
    date accessioned2017-05-08T23:56:47Z
    date available2017-05-08T23:56:47Z
    date copyrightApril, 1998
    date issued1998
    identifier issn0094-4289
    identifier otherJEMTA8-26991#131_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/120529
    description abstractIt is shown that there exist approximations of the Hencky (logarithmic) finite strain tensor of various degrees of accuracy, having the following characteristics: (1) The tensors are close enough to the Hencky strain tensor for most practical purposes and coincide with it up to the quadratic term of the Taylor series expansion; (2) are easy to compute (the spectral representation being unnecessary); and (3) exhibit tension-compression symmetry (i.e., the strain tensor of the inverse transformation is minus the original strain tensor). Furthermore, an additive decomposition of the proposed strain tensor into volumetric and deviatoric (isochoric) parts is given. The deviatoric part depends on the volume change, but this dependence is negligible for materials that are incapable of large volume changes. A general relationship between the rate of the approximate Hencky strain tensor and the deformation rate tensor can be easily established.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleEasy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate
    typeJournal Paper
    journal volume120
    journal issue2
    journal titleJournal of Engineering Materials and Technology
    identifier doi10.1115/1.2807001
    journal fristpage131
    journal lastpage136
    identifier eissn1528-8889
    keywordsTensors
    keywordsApproximation
    keywordsCompression
    keywordsTension AND Deformation
    treeJournal of Engineering Materials and Technology:;1998:;volume( 120 ):;issue: 002
    contenttypeFulltext
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