| Popis: |
We derive a dimensionally reduced model for a thin film prestrained with a given incompatible Riemannian metric: ¶ G h ( x ′ , x 3 ) = I 3 + 2 h γ S ( x ′ ) + 2 h γ ∕ 2 x 3 B ( x ′ ) + higher order terms , γ > 2 , ¶ where [math] is the thickness of the film. The problem is studied rigorously by using a variational approach and establishing the [math] -convergence of the non-Euclidean version of the nonlinear elasticity functional. It is shown that the residual nonlinear elastic energy scales as [math] as [math] . |
