Computational finite element model for surface wrinkling of shells on soft substrates

• Published in: Communications in nonlinear science & numerical simulation 2019-11, Vol.78, p.104863, Article 104863
• Main Authors: Veldin, Tomo, Brank, Boštjan, Brojan, Miha
• Format: Article
• Language: English
• Subjects: Film-substrate composite; Model order reduction; Surface wrinkling; Thin shells
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.104863

•A robust computational model for wrinkling of shell-core systems was developed.•Shells of general shape subjected to external pressure can be analyzed.•Wrinkling patterns on spheres, hemispheres and spheroids were studied.•A good match between experiments and numerical prediction was demonstrated. We provide a robust finite element formulation for quantitative prediction of surface wrinkling of pressurized elastic shells on soft substrates. Our theory is build on three basic assumptions which involve thin shell kinematics, the approximation of the substrate response by a Winkler foundation and a model order reduction of the displacement field. Our element keeps all the nonlinear terms of the reduced model. The proposed formulation does not require any perturbations, either in the initial geometry or in the load, to incite the transition from fundamental to secondary equilibrium path for the considered set of shells, due to inherent asymmetric imperfections in the mesh. Numerical simulations using the derived element and an advanced path-following method on full spheres, hemispheres and spheroids show a very good quantitative agreement with theoretical predictions and experiments on the characteristic wavelength of the pattern as well as the qualitative depiction of the pattern evolution.