Effect of prestrains on swelling-induced buckling patterns in gel films with a square lattice of holes

Abstract

We investigate the effect of prestrains on swelling-induced buckling patterns in polymeric films with a square lattice of holes. To reproduce experiments conducted by Zhang et al. (2008), poly(dimethylsiloxane) (PDMS) films are pre-strained in in-plane uniaxial tension in a lattice direction, and subsequently swelled by toluene. Finite element analysis is performed using an inhomogeneous field theory of polymeric gels in equilibrium, and with the aid of artificial damping. Periodic units consisting of 2×2 and 10×10 unit cells are analyzed under a generalized plane strain assumption. Analysis of the 10×10 unit cell shows that the resulting buckling pattern depends on the increase in prestrain of ε=0, 0.2, 0.4 and 0.6, evolving as a diamond plate pattern (ε=0), a slightly distorted diamond plate pattern (ε=0.2), a binary pattern of circles and lines (ε=0.4), and a monotonous pattern of ellipses (ε=0.6). These predictions are in very good agreement with experiments. The 2×2 unit cell reveals that these different patterns appear continuously as transitional states during transformation into diamond plate patterns; prestrains in uniaxial tension delay the onset of the pattern transformation and equilibrium swelling interrupts the progress of the transformation. Parametric studies demonstrate that the pattern dependence on prestrains originates from intrinsic swelling features, and is a consequence of a particular combination of the selected polymer and solvent.