Delamination of cylindrical shells from soft and adhesive Winkler’s foundation

  Oz Oshri  
Department of Mechanical Engineering, Ben-Gurion University of the Negev

The interaction between thin elastic films and soft-adhesive foundations has recently gained interest due to technological applications that require control over such objects. Motivated by these applications we investigate the equilibrium configuration of a cylindrical shell with natural curvature κ and bending modulus B, that is adhered to soft and adhesive foundation with stiffness K. We derive an analytical model that predicts the delamination criterion, i.e., the critical natural curvature, κcr  , at which delamination first occurs, and the ultimate shape of the shell. While in the case of a rigid foundation, K → ∞, our model recovers the known, two states, solution, at which the shell either remains completely attached to the substrate or completely detaches from it, on a soft foundation our model predicts the emergence of a new branch of solutions. This branch corresponds to partially adhered shells, where the contact zone between the shell and the substrate is finite and scales as  lw∼(B/K)1/4 . In addition, we find that the criterion for delamination depends on the total length of the shell along the curved direction, L. While relatively short shells, L ∼ lw, transform continuously between adhered and delaminated solutions, long shells, L»lw , transform discontinuously. Notably, our work provides insights into the detachment phenomena of thin elastic sheets from soft and adhesive foundations.