Deformation of a sheet with coupling between elasticity and concentration.
We investigate a simple model for equilibrium deformation of a sheet with concentration-dependent elasticity. The model is motivated by several physical situations where deformation of a sheet is modulated by concentration of a mobile species, for example, a quasi-2D array of carbon nanotubes. Elasticity of the sheet is modeled using a free energy functional that includes concentration-dependent potential energies, and a free energy of mixing. We show that the sheet responds to imposed distortion by rearranging its constituents and can do so in a smooth and stable manner only for sufficiently small distortion. For larger distortions, through phase plane and numerical analysis, we consider how the system can meet boundary conditions through nonsmooth solutions.
Khripin
Constantine
C
Department of Chemical Engineering, Lehigh University, 111 Research Drive, Bethlehem, Pennsylvania 18015, USA.
Tang
Tian
T
Jagota
Anand
A