A rational reduced model for elastic layers and its application in pattern formation analysis

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Stress-induced wrinkling patterns at micro- and sub-micro-scales have a growing variety of applications ranging from cell patterning, optical gratings, creation of surfaces with desired wetting and adhesion properties, to buckling-based metrology. Although much progress has been made in recent decades, a deeper understanding of the pattern formation mechanisms has been hampered by the complexity of the governing equations. This proposal aims tobreak a bottleneck in the mathematical modelling of pattern formation in film-substrate bilayers. We will derive a rational reduced model for the film behaviour under the frameworks of nonlinear elasticity and Stroh formalism that incorporates nonlinearity, anisotropy, and pre-stretch in a self-consistent manner. The power of the new model will be illustrated by analysing period-doubling secondary bifurcation and ridge formation that have been much studied but not yet fully understood.