We propose an efficient computational model for predicting the surface wrinkling in axially compressed bi-layer cylindrical shell-substrate composites. To capture the transitions between the ...wrinkling modes in the far post-buckling regime, we use implicit dynamics. In this context we apply a generalized and an energy-decaying time stepping schemes that numerically dissipate in the high frequency range. The other components of the model are a geometrically exact, rotation-less, nonlinear shell finite element for the cylinder and an elastic foundation that represents the substrate. We show that the proposed computational model predicts the wrinkling pattern transition from axisymmetric to diamond-like mode, which is consistent with the numerical and laboratory experiments reported earlier. Furthermore, the results of our computational model show the existence of several diamond-like mode jumps in the post-buckling regime, a result that has not yet been reported for the axially compressed shell-substrate cylinders.
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