Non-Oscillation Criteria for Hypoelastic Models under Simple Shear Deformation
Resource
Journal of Elasticity, Vol.57, pp.201-241
Journal
Journal of Elasticity
Journal Volume
Vol.57
Pages
201-241
Date Issued
1999
Date
1999
Author(s)
Chein-Shan Liu
Abstract
Ten objective rates, spinning or non-spinning, are critically examined from the viewpoint of Sturm's theorems in ordinary differential equations. Upon developing implication relations of oscillatory, non-oscillatory, and disconjugate behavior, we establish oscillation and non-oscillation criteria which pick out the objective stress rates that lead to oscillatory and non-oscillatory responses in simple shear deformation, respectively. Among the hypoelastic equations associated with the spinning objective rates examined, the Jaumann equation is an oscillatory minorant, the homogeneous Xiao-Bruhns-Meyers equation is a non-oscillatory majorant, and the homogeneous Green-Naghdi equation is a disconjugate majorant. If (Sturm comparable) non-spinning objective rates are also taken into consideration, then the Durban-Baruch equation becomes an oscillatory minorant, but the other two equations remain to play the same roles. The Jaumann equation is a Sturm majorant for all the other nine homogeneous hypoelastic equations, and the homogeneous Szabo-Balla-2 equation is a Sturm minorant for all the other nine homogeneous hypoelastic equations. Most of the solutions of the zeroth-grade hypoelastic equations at simple shear have already been published, except for those of Szabo and Balla, to which the closed-form solutions are derived here. Moreover, all solutions are extended to include the effect of initial stresses.
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
Journal of Elasticity, Vol.57, pp.201-241.pdf
Size
293.06 KB
Format
Adobe PDF
Checksum
(MD5):275d01b80483554be7e32bddfe23ebfb