Determining the elastic modulus of thin films using a buckling-based method: computational study

The buckling mode of a thin film lying on a soft substrate has been used to determine the elastic modulus of thin films and one-dimensional objects (e.g. nanowires and nanotubes). In this paper, dimensional analysis and three-dimensional nonlinear finite element computations have been made to investigate the buckling of a film with finite width bonded to a compliant substrate. Our study demonstrates that the effect of Poisson's ratio of the film can be neglected when its width-thickness ratio is smaller than 20. For wider films, omitting the influence of Poisson's ratio may lead to a significant systematic error in the measurement of the Young's modulus and, therefore, the film should be treated as a plate. It is also found that the assumption of the uniform interfacial normal stress along the width of the film made in the theoretical analysis does not cause an evident error, even when its width is comparable to its thickness. Based on the computational results, we further present a simple expression to correlate the buckling wavelength with the width and thickness of the film and the material properties (Young's moduli and Poisson's ratios) of the film and substrate, which has a similar form to that in the classical plane-strain problem. The fundamental solutions reported here are not only very accurate in a broad range of geometric and material parameters but also convenient for practical use since they do not involve any complex calculation.