Boudaoud A, Patrício P, Couder Y, Amar M B
Laboratoire de Physique Statistique de l'ENS, Paris, France.
Nature. 2000 Oct 12;407(6805):718-20. doi: 10.1038/35037535.
Large deformations of thin elastic plates usually lead to the formation of singular structures which are either linear (ridges) or pointlike (developable cones). These structures are thought to be generic for crumpled plates, although they have been investigated quantitatively only in simplified geometries. Previous studies have also shown that a large number of singularities are generated by successive instabilities. Here we study, experimentally and numerically, a generic situation in which a plate is initially bent in one direction into a cylindrical arch, then deformed in the other direction by a load applied at its centre. This induces the generation of pairs of singularities; we study their position, their dynamics and the corresponding resistance of the plate to deformation. We solve numerically the equations describing large deformations of plates; developable cones are predicted, in quantitative agreement with the experiments. We use geometrical arguments to predict the observed patterns, assuming that the energy of the plate is given by the energy of the singularities.
薄弹性板的大变形通常会导致奇异结构的形成，这些结构要么是线性的（脊），要么是点状的（可展锥）。尽管仅在简化几何形状中对这些结构进行了定量研究，但人们认为它们是褶皱板的常见特征。先前的研究还表明，连续的不稳定性会产生大量奇点。在这里，我们通过实验和数值方法研究一种常见情况：一块板最初在一个方向上弯曲成圆柱拱，然后通过在其中心施加的载荷在另一个方向上变形。这会诱导奇点对的产生；我们研究它们的位置、动力学以及板对变形的相应抵抗力。我们通过数值方法求解描述板大变形的方程；预测出了可展锥，与实验结果在定量上相符。我们使用几何论证来预测观察到的图案，假设板的能量由奇点的能量给出。
