Semi-analytical solution for deformation of elastic/viscoelastic two-layered films pressed on partially-opened substrate. (15th May 2020) - Shiratori, Suguru; Nagano, Hideaki; Shimano, Kenjiro
Abstract: This paper proposes an efficient solution procedure for the deformation of a viscoelastic film pressed by another elastic film in cases wherein the films are on partially-opened substrates. The problem is formulated as a quasi-static stress state, where the stress equilibrium is satisfied at each time instance. The instantaneous stress equilibrium is expressed by biharmonic and harmonic functions for the stress and displacement of those general solutions that can be obtained in the Fourier domain. By applying the boundary conditions mathematically everywhere but the surface, which is in direct contact with the partially-opened substrate, the total problem could be discretized and solved using the Fourier collocation method. In this manner, the total number of unknowns can be greatly reduced. The validity and effectiveness of the proposed method was confirmed by comparing the results with those obtained by a finite element method (FEM) solver. The viscoelastic deformation obtained by the proposed method was almost in complete agreement with the result obtained by the FEM. The elapsed computational time required by the proposed method was approximately 1/100 of that required by the FEM.