The analytical solution is obtained for a semi-infinite linear elastic solid with a sinusoidal, “wavy” surface profile subject to applied strain. The amplitude A of a deformed wavy surface is related to the initial amplitude A0 and the applied strain εa through the simple expression A=A0(1−εa). This relation is confirmed independently by finite element analyses and experimental measurements of strained wavy poly(dimethylsiloxane) surfaces. Analytical solutions are also obtained for a wavy solid subject to stretch and lateral displacement.
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Xiao et al. (2009) studied this question.
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