Non-ideal effects in bending response of soft substrates covered with biomimetic scales

Biomimetic scales are known to substantially alter the mechanics response of the underlying substrate engendering complex nonlinearities that can manifest even in small deformations due to scales interaction. This interaction is typically modeled using a-priori homogenization with an enforced periodicity of engagement. Such a framework is fairly useful especially when dealing with the structural length scale which is at least one order of magnitude greater than the scales themselves since individual tracking of a large number of scales become insurmountable. On the other hand, this scheme makes several assumptions whose validity has not yet been investigated including infinite length of the substrate and rigidity of the scales. The validity of these assumptions and the accuracy and limitations of associated analytical models are investigated. Finite element based numerical studies were carried out to identify the critical role of edge effects and other non-ideal behavior such as violation of periodicity and nonlinear constitutive response on scale rotation. Our investigation shows that several important quantities show a strong saturation characteristic which justify many of the simplifying assumptions whereas others need much greater care.