Metric-induced morphogenesis and non-euclidean elasticity: Scaling laws and thin film models

Abstract

The purpose of this paper is to report on recent developments concerning the analysis and the rigorous derivation of thin film models for structures exhibiting residual stress at free equilibria. This phenomenon has been observed in different contexts: growing leaves, torn plastic sheets and specifically engineered polymer gels. The study of wavy patterns in these contexts suggest that the sheet endeavors to reach a non-attainable equilibrium and hence assumes a non-zero stress rest configuration.