Postcritical imperfection sensitivity of sandwich or homogenized orthotropic columns soft in shear and in transverse deformation

The previous energetic variational analysis of critical loads and of the choice of finite strain measure for structures very weak in shear, remaining in a state of small strain, is extended to the initial postcritical behavior. For this purpose, consideration of the transverse deformation is found to be essential. It is shown that imperfection sensitivity of such structures, particularly laminate-foam sandwich plates, can arise for a certain range of stiffness and geometric parameters, depending on the proper value of parameter m of the Doyle–Ericksen finite strain tensor, as determined in the previous analysis. The bifurcation is symmetric and Koiter’s 2/3-power law is followed. The analytical predictions of maximum load reductions due to imperfection sensitivity are verified by finite element simulations. The possibility of interaction between different instability modes, particularly lateral deflection and bulging, is also explored, with the conclusion that lateral deflection dominates in common practical situations.