Stability and finite strain of homogenized structures soft in shear: Sandwich or fiber composites, and layered bodies

The stability theories energetically associated with different finite strain measures are equivalent if the tangential moduli are transformed as a function of the stress. However, for homogenized soft-in-shear composites, they can differ greatly if the material is in small-strain and constant elastic moduli measured in small-strain tests are used. Only one theory can then be correct. The preceding variational energy analysis showed that, for sandwich columns and elastomeric bearings, respectively, the correct theories are Engesser s and Haringx s, associated with Green s and Almansi s Lagrangian strain tensors, respectively. This analysis is reviewed, along with supporting experimental and numerical results, and is then extended to arbitrary multiaxially loaded homogenized soft-in-shear orthotropic composites. It is found that, to allow the use of constant shear modulus when the material is in small strain, the correct stability theory is associated with a general Doyle–Ericksen finite strain tensor of exponent m depending on the principal stress ratio. Further it is shown that the standard updated Lagrangian algorithm for finite element analysis, which is associated with Green s Lagrangian finite strain, can give grossly incorrect results for homogenized soft-in-shear structures and needs to be generalized for arbitrary finite strain measure to allow using constant shear modulus for critical loads at small strain.