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.
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April 1998
Technical Papers
Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate
Zdeneˇk P. Bazˇant
Zdeneˇk P. Bazˇant
Northwestern University, Evanston, IL 60208
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Zdeneˇk P. Bazˇant
Northwestern University, Evanston, IL 60208
J. Eng. Mater. Technol. Apr 1998, 120(2): 131-136 (6 pages)
Published Online: April 1, 1998
Article history
Received:
January 12, 1997
Revised:
November 24, 1997
Online:
November 27, 2007
Citation
Bazˇant, Z. P. (April 1, 1998). "Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate." ASME. J. Eng. Mater. Technol. April 1998; 120(2): 131–136. https://doi.org/10.1115/1.2807001
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