非对称薄膜的形变
Deformation of an asymmetric thin film
摘要：
实验研究了化学蒸气不对称膨胀引起的聚合物膜形状变化。受到最近关于非欧几里得度量塑造弹性片的工作的启发[Y。Klein，E. Efrati和E. Sharon，Science 315，1116（2007）]，我们通过目标度量张量的变化来表示化学蒸气的影响。在这个问题中，与先前的工作不同，目标度量在膜的两侧之间是不对称的。改变该度量引起膜的曲率，其可以是弯曲成部分圆柱体或部分球体。我们计算这些形状的弹性能量，并表明，球体是有利于小于临界尺寸的薄膜，这取决于薄膜厚度，而圆柱体是有利于较大的薄膜。
英文摘要：
Experiments have investigated shape changes of polymer films induced by asymmetric swelling by a chemical vapor. Inspired by recent work on the shaping of elastic sheets by non-Euclidean metrics [Y. Klein, E. Efrati, and E. Sharon, Science 315, 1116 (2007)], we represent the effect of chemical vapors by a change in the target metric tensor. In this problem, unlike that earlier work, the target metric is asymmetric between the two sides of the film. Changing this metric induces a curvature of the film, which may be curvature into a partial cylinder or a partial sphere. We calculate the elastic energy for each of these shapes, and show that the sphere is favored for films smaller than a critical size, which depends on the film thickness, while the cylinder is favored for larger films.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
