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

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.