Shaping of elastic sheets by prescription of non-Euclidean metrics
Shaping of elastic sheets by prescription of non-Euclidean metrics
复制标题
DOI：
10.1126/science.1135994
复制
发表时间：
2007-02-23
期刊：
影响因子：
56.9
通讯作者：
Sharon, Eran
中科院分区：
文献类型：
--
作者：
Klein, Yael;Efrati, Efi;Sharon, Eran
表面度量与其高斯曲率（高斯定理）之间的联系为局部生长或收缩弹性片的成形原理提供了基础。我们构建了横向不均匀收缩的薄凝胶片。这种差异收缩规定了板材上的非欧几里得度量。为了最大限度地减少弹性能，自由片材形成遵循所施加的度量的三维结构。我们展示了大规模屈曲和多尺度起皱结构是如何出现的，具体取决于规定指标可能嵌入的性质。我们进一步提出了如何生成每种类型特征的指南。
The connection between a surface's metric and its Gaussian curvature ( Gauss theorem) provides the base for a shaping principle of locally growing or shrinking elastic sheets. We constructed thin gel sheets that undergo laterally nonuniform shrinkage. This differential shrinkage prescribes non-Euclidean metrics on the sheets. To minimize their elastic energy, the free sheets form three-dimensional structures that follow the imposed metric. We show how both large-scale buckling and multiscale wrinkling structures appeared, depending on the nature of possible embeddings of the prescribed metrics. We further suggest guidelines for how to generate each type of feature.