Matsumoto Elisabetta A, Kamien Randall D
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 1):021604. doi: 10.1103/PhysRevE.80.021604. Epub 2009 Aug 12.
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple model for determining the orientational order of such patterns using only linear elasticity theory which correctly predicts the outcomes of several experiments. Each element of the pattern is modeled by a "dislocation dipole" located at a point on a lattice, which then interacts elastically with all other dipoles in the system. We explicitly consider a membrane with a square lattice of circular holes under uniform compression and examine the changes in morphology as it is allowed to relax in a specified direction.
最近的实验利用了膜中的弹性不稳定性来创建复杂图案。然而，由于这些结构是非线性弹性行为的产物，对其进行合理设计面临诸多挑战。我们提出了一个简单模型，仅使用线性弹性理论来确定此类图案的取向有序性，该模型能正确预测多个实验的结果。图案的每个元素由位于晶格上某点的“位错偶极子”建模，然后它与系统中的所有其他偶极子进行弹性相互作用。我们明确考虑一个具有均匀压缩下圆形孔正方形晶格的膜，并研究其在特定方向上松弛时形态的变化。
