Modelling the dynamics of shape change in a patterned viscoelastic sheet

There is a wide-scale interest in the study of material sheets that change their 3D shape on being stimulated. Examples include liquid crystal elastomers that deform upon heat or light variations or monolayer epithelia that deform during the development of an organism. Previous studies have dealt with the equilibrium geometry and energy description of shape changes within the framework of elasticity theory. In our study, we take a different direction by introducing viscoelasticity and studying the dynamics analytically and in spring-dashpot lattice simulations. As an example, we study a frustrated flat sheet that relaxes into semi-spherical configuration. We trace the dynamics of our simulations and show that the geometry of the final shape is independent of the viscoelastic parameters. Our simulations reveal the emergence of a characteristic time-scale before appearance of curvature, reminiscent of the classical buckling transition, where beyond a critical thickness, the sheet stays flat in order to avoid high bending energy. Finally, we discuss the dependence of this time-scale on the viscoelastic coefficients and show that adding spatial variability in the viscoelastic parameters leads to disappearance in this delay in appearance of curvature while retaining the final shape.