Surface wrinkling of a hyperelastic half-space coated by a liquid crystal elastomer film

Abstract

We consider the stability of a hyperelastic substrate coated by a liquid crystal elastomer film and subjected to compressive forces. In this problem, the liquid crystal elastomer directors are free to evolve and this possible variation needs to be included in the stability analysis. We consider the case where the initial directors are aligned either in the horizontal or in the vertical direction and obtain an exact bifurcation condition for surface wrinkling. We show that director reorientation increases both the critical compressive strain and the critical wavenumber, hence stabilizing the material. In the small wavenumber limit we carry out an asymptotic analysis and obtain analytical solutions for the critical stretch and the critical wavenumber, which can be useful in applications.