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TECHNICAL BRIEFS

# Which Formulation Allows Using a Constant Shear Modulus for Small-Strain Buckling of Soft-Core Sandwich Structures?

[+] Author and Article Information
Zdeněk P. Bažant

Northwestern University, 2145 Sheridan Road, CEE, Evanston, IL 60208z-bazant@northwestern.edu

Alessandro Beghini

Northwestern University, Evanston, IL 60208a-beghini@northwestern.edu

J. Appl. Mech 72(5), 785-787 (Dec 30, 2004) (3 pages) doi:10.1115/1.1979516 History: Received April 06, 2004; Revised December 30, 2004

## Abstract

Although the stability theories energetically associated with different finite strain measures are mutually equivalent if the tangential moduli are properly transformed as a function of stress, only one theory can allow the use of a constant shear modulus $G$ if the strains are small and the material deforms in the linear elastic range. Recently it was shown that, in the case of heterogeneous orthotropic structures very soft in shear, the choice of theory to use is related to the problem of proper homogenization and depends on the type of structure. An example is the difference between Engesser’s and Haringx’s formulas for critical load of columns with shear, which were shown to be energetically associated with Green’s and Almansi’s Lagrangian finite strain tensors. In a previous brief paper of the authors in a conference special issue, it was concluded on the basis of energy arguments that, for constant $G$, Engesser’s formula is correct for sandwich columns and Haringx’s formula for elastomeric bearings, but no supporting experimental results were presented. To present them, is the main purpose of this technical brief.

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## Figures

Figure 1

Column in (a) initial state, (b) deflected state; contribution to the shear deformation of a sandwich beam element: (c) bending, and (d) shear

Figure 2

Comparison of buckling formulas and experimental results for various density of Divinycell foam

Figure 3

Contribution to the shear deformation of an elastomeric bearing element: (a) initial state, (b) bending, and (c) shear

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