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

[+] Author and Article Information
Zdeněk P. Bažant

Northwestern University, Evanston, IL 60208

J. Eng. Mater. Technol 120(2), 131-136 (Apr 01, 1998) (6 pages) doi:10.1115/1.2807001 History: Received January 12, 1997; Revised November 24, 1997; Online November 27, 2007


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.

Copyright © 1998 by The American Society of Mechanical Engineers
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