A two-dimensional Fourier-series finite element for wrinkling analysis of thin films on compliant substrates. (May 2017) - Huang, Qun; Xu, Rui; Liu, Yin; Hu, Heng; Giunta, Gaetano; Belouettar, Salim; Potier-Ferry, Michel
Abstract: In this paper, an efficient Fourier-series finite element solution framework is proposed to simulate the wrinkling phenomena in two-dimensional film/substrate system. In the method, the displacement field is transformed into the slowly variable Fourier coefficient, i.e., the macroscopic displacement field, which permits to capture the wrinkling evolution in the system with much less degrees of freedom than the full finite element model. The derived macroscopic non-linear system is solved by the Asymptotic Numerical Method that is very efficient and reliable to capture the bifurcation point and the post-buckling path in wrinkling analyses. In particular, the importance of using the first harmonic of Fourier series in approximating the axial displacement in substrate is discussed and a spurious phenomenon related to the hypothesis of the used approximation functions within the Fourier-series approach, i.e., oscillation locking, is pointed out. To overcome this phenomenon, modifications on either the Fourier series or the constitutive equations of the substrate are proposed. The efficiency and accuracy of the proposed macroscopic model are demonstrated by the wrinkling simulations for several kinds of film/substrate systems. Abstract : Highlights: We use Fourier series to establish a macroscopic model for instability phenomena in film/substrate system. The macroscopic model correctly predicts the wrinkling patterns with a reduced computational cost. The importance of the first harmonic of Fourier series in continuum elements is discussed. A spurious phenomenon named oscillation locking is pointed out and two efficient methods are proposed to overcome the locking effect.