Sensitivity of the post-localization response of a thick cross-ply imperfect ring to transverse Young’s modulus nonlinearity

A fully nonlinear finite elements analysis for prediction of localization (onset of deformation softening) and post-localization response of a thick cross-ply [90/0/90] imperfect plane strain ring (infinitely long cylindrical shell) under applied hydrostatic pressure is presented. The present investigation is concerned with the prediction of post-“yield” and post-localization equilibrium paths for moderately thick and thick cross-ply rings, which are often unstable in the presence of modal imperfections and material nonlinearity, and which are considered to “bifurcate” from the primary equilibrium paths, representing periodic buckling patterns pertaining to global or structural level stability. The present nonlinear finite element solution methodology, based on the total Lagrangian formulation, employs a quasi-three-dimensional hypothesis, 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 (hypoelastic) material property for the transverse Young’s modulus, ETT, on the localization phenomenon are thoroughly investigated, and physically meaningful conclusions are drawn from these numerical results.