Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its RateSource: Journal of Engineering Materials and Technology:;1998:;volume( 120 ):;issue: 002::page 131Author:Zdeněk P. Bažant
DOI: 10.1115/1.2807001Publisher: 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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contributor author | Zdeněk P. Bažant | |
date accessioned | 2017-05-08T23:56:47Z | |
date available | 2017-05-08T23:56:47Z | |
date copyright | April, 1998 | |
date issued | 1998 | |
identifier issn | 0094-4289 | |
identifier other | JEMTA8-26991#131_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/120529 | |
description 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. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate | |
type | Journal Paper | |
journal volume | 120 | |
journal issue | 2 | |
journal title | Journal of Engineering Materials and Technology | |
identifier doi | 10.1115/1.2807001 | |
journal fristpage | 131 | |
journal lastpage | 136 | |
identifier eissn | 1528-8889 | |
keywords | Tensors | |
keywords | Approximation | |
keywords | Compression | |
keywords | Tension AND Deformation | |
tree | Journal of Engineering Materials and Technology:;1998:;volume( 120 ):;issue: 002 | |
contenttype | Fulltext |