Buckling versus folding: Importance of viscoelasticity

Abstract

We present a dominant wavelength solution for a viscoelastic layer embedded in a low viscosity matrix under layer‐parallel compression based on the thin‐plate approximation. We show that the deformation mode approximates the elastic or viscous limits depending on a parameter, R, which is the ratio of dominant wavelength predicted by pure viscous theory to the one predicted by pure elastic theory. In contrast, conventional analyses based on the Deborah number incorrectly predict the deformation mode. The dominant viscoelastic wavelength closely follows the minimum out of viscous and elastic dominant wavelengths. The viscoelastic thin‐plate theory is verified by two‐dimensional modeling of large strain viscoelastic folding, for which we develop a new numerical algorithm based on a combined spectral/finite‐difference method. The robustness of the numerical code is demonstrated by calculation, for the first time, of the pressure field evolution during folding of a viscoelastic layer with up to 100% strain.