School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138.
Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel 91904
Proc Natl Acad Sci U S A. 2020 May 12;117(19):10195-10202. doi: 10.1073/pnas.1920237117. Epub 2020 Apr 29.
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to their nonlinear mechanics and the presence of nontrivial geometrical effects. While numeric approaches are successful, analytic tools and conceptual frameworks are largely lacking. Using an analogy with electrostatics, and building on recent developments in a nonlinear geometric formulation of elasticity, we develop a formalism that maps the two-dimensional (2D) elastic problem into that of nonlinear interaction of elastic charges. This approach offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability, and aspects of the postinstability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical 2D structures. Possible applications of the tools developed in this work for the study of ordered and disordered 2D porous elastic metamaterials are discussed.
柔性机械超材料以及一般的高可变形多孔固体的问题非常丰富和复杂，这是由于它们的非线性力学和复杂的几何效应。虽然数值方法是成功的，但分析工具和概念框架在很大程度上是缺乏的。我们利用静电学的类比，并基于弹性的非线性几何表述的最新进展，开发了一种形式体系，将二维（2D）弹性问题映射到弹性电荷的非线性相互作用问题。这种方法提供了一个直观的概念框架，可以定性地解释线性响应、力学不稳定性的出现以及失稳后的状态的某些方面。除了直观的解释，该形式体系还定量地再现了几个典型 2D 结构的全数值模拟。本文还讨论了所开发的工具在有序和无序 2D 多孔弹性超材料研究中的可能应用。
