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Effects of geometrical imperfection on swelling induced buckling patterns of gel film with square lattice of holes

Dai Okumura (Nagoya University), Tsuyoshi Kuwayama (Nagoya University), Nobutada Ohno (Nagoya University)

Instability in Solids and Structures

Tue 9:00 - 10:30

Barus-Holley 190

In this study, we investigate effects of geometrical imperfection on swelling induced buckling patterns of a gel film with a square lattice of holes. Finite element analysis is performed using the inhomogeneous field theory in equilibrium proposed by Hong et al., (2009), in which Flory-Rehner free energy function (1943) is applied to swelling elastomers. Periodic units consisting of 2x2 or 10x10 unit cells are analyzed under a generalized plane strain assumption. Geometrical imperfection is introduced by considering randomly oriented elliptic holes, and the degree of pattern formulation is quantified by using a measure of deviation from roundness. Results of 2x2 unit cells show that three characteristic buckling patterns can arise depending on randomness, although the most dominant one is the diamond plate pattern, which was observed in experiments (Zhang et al., 2008). In contrast, results of 10x10 unit cells predict the diamond plate pattern in all random cases. It is shown that this homogeneous pattern transformation in the large periodic unit is a consequence of propagation of a locally induced diamond plate structure. References: Hong, W., Liu, Z., Suo, Z., 2009. Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solids and Structures, Vol.46, pp.3282-3289. Flory, P.J., Rehner, J., 1943. Statistical Mechanics of cross-linked polymer networks, II. swelling. The Journal of Chemical Physics, Vol.11, pp.521-526. Zhang, Y., Matsumoto, E.A., Peter, A., Lin, P.-C., Kamien, R.D., Yang, S., 2008. One-step nanoscale assembly of complex structures via harnessing of an elastic instability. Nano Letters, Vol.8, pp.1192-1196.