Three-dimensional analysis of the spontaneous instability for soft thin viscoelastic films

Based on the continuum mechanics and the bifurcation theory, a three-dimensional theoretical model for a soft thin viscoelastic film bonded to a rigid substrate is investigated. Considering the competition among van der Waals interaction potential energy, strain energy, and surface energy, three-dimensional governing equations of the spontaneous instability are derived, and the analytical results of time-dependent critical conditions are obtained. Furthermore, the phase diagram of instability due to van der Waals interaction and variation of the dimensionless characteristic wavenumber and the critical stiffness of interaction with the critical time are discussed.