Statics of wrinkling films

An analytical investigation of the equilibrium of wrinkling films is conducted. Zak (1979) has shown that wrinkling occurs in connection with the instability of a smooth film having no resistance to bending in the case of compression. The governing equation for the equilibrium of a film with possible regions of wrinkling is considered. The introduction of fictitious stress reduces the governing equation to a form which formally coincides with the governing equation for a string. Equilibrium conditions in the case of an absence of external forces are explored, taking into account the stretching of a semispherical film, the torsion of a convex film of revolution, and stress singularities. A study is conducted of the equilibrium under conditions in which external forces normal to the surface of a film are present. Attention is also given to the equilibrium in a potential field.