Effects of thickness and transverse shear modulus nonlinearity on the post-“yield” and post-localization response of an externally pressurized imperfect cross-ply ring

The present investigation is concerned with the prediction of localization (onset of deformation softening) and post-localization and post-“yield” equilibrium paths for moderately thick and thick cross-ply [90/0/90] imperfect plane strain rings. These paths are often unstable in the presence of modal imperfections and material nonlinearity, and are considered to “bifurcate” from the primary equilibrium paths, representing periodic buckling patterns pertaining to global or structural level stability. The fully nonlinear finite element analysis, based on the total Lagrangian formulation, employs a three-dimensional theory, known as layer-wise linear displacement distribution theory (LLDT), to capture the three-dimensional interlaminar (especially, shear) deformation behavior, associated with the localized interlaminar shear-crippling failure. The combined effects of modal imperfections, interlaminar shear/normal deformation and nonlinear (hypo-elastic) material property for the transverse shear modulus, GTT, on the localization and delocalization (deformation hardening) phenomena are thoroughly investigated, and physically meaningful conclusions are drawn from these numerical results.