有限尺寸硬薄膜/软基底的屈曲分析

Buckling Analysis of Finite Stiff Film/Soft Substrate System

附着在柔软基体之上的硬薄膜,在受轴向压缩超过临界值时会发生屈曲,在表面产生褶皱.根据Kirchhoff-Love板理论和最小势能原理,分析了有限尺寸薄膜/无限大基底结构的几何尺寸及材料常数对屈曲行为的影响.结果表明临界屈曲应变随薄膜泊松比或薄膜宽度的增大而增大;当薄膜长度较小时,临界屈曲应变随薄膜长度的改变而呈现振荡式变化,而当薄膜长度较大时,临界屈曲应变趋于定值.同时,薄膜泊松比的增大会导致褶皱幅值略微减小,但不改变幅值与波长之比;薄膜宽度的增加会使得褶皱幅值在沿宽度方向变化更明显;当外加应变较小时,褶皱幅值随弹性常数比的增大而增大,当外加应变较大时,褶皱幅值受弹性常数比的影响变得微弱.

A stiff film bonded to a soft substrate subjected to uniaxial compression will form wrinkles. Following Kirchhoff-Love plate theory and principle of minimum potential energy, we analyzed how geometric dimensions and material modulus affect the buckling morphology. We showed that the critical strain increases as the Poisson＇s ratio or the width of the film increases. When the film is short, the critical strain varies with the film length in a oscillatory mode, while when the film is long, the critical strain tends to be constant. The increase of Poisson＇s ratio of film causes slight decrease of the wrinkle amplitude, but does not affect the ratio of amplitude to wavelength. The amplitude also varies more clearly along the width direction as the width of film increases. When the applied strain is small, the amplitude increases as the modulus ratio increases; while when the applied strain is large, the modulus ratio imposes little influence on the amplitude.