Numerical studies on stretch-induced and shear-induced wrinkles of hyperelastic membranes based on a uniformly-valid asymptotic plate theory

Abstract

In this paper, we study the stretch-induced and shear-induced wrinkles of rectangular hyperelastic membranes numerically based on the weak forms of the uniformly-valid asymptotic plate theory. To trigger wrinkling bifurcation, we impose two small and different forms of imperfection loads on the top surface of the membrane when the membrane is subjected to stretching or shearing, respectively. For the case of stretching, we obtain the first and secondary critical bifurcation points and wrinkled configurations. The effects of microstructure in membrane are also analyzed numerically. For the case of shearing, the numerical solutions can be obtained easily for various pretension displacements including the nearly slack and completely slack membranes. The numerical results show that the pretension displacements could affect the critical shear displacement, the amplitude and the number of wrinkles. The numerical results for both cases are consistent with those in the literature.