A Microtwist Theory of Polarized Mechanical Metamaterials: Modeling and Experiments

基于晶格的超材料是一种具有定义结构的材料，它让人想起原子晶格，但在更大的长度尺度上。这些材料通常表现出独特的功能，可以追溯到它们的微建筑设计。现代制造技术的进步以及越来越环保的设计约束推动了基于晶格的机械超材料的研究，这些材料提供了一系列天然材料不寻常的性能。为了使其能够使用，必须对基础桁架的组成，几何形状和整体形态如何在宏观尺度（厘米到米）上控制所需和目标的机械性能有一个很好的理解。本提案旨在设计、建模和测试极化晶格超材料：在处处具有相同微观结构的同时，它们仍然设法在一侧对压痕柔软，而在另一侧对压痕坚硬。电极化是连续电动力学的一个经典概念，而弹性静力学和弹性动力学中的机械极化已经脱离了早期理论的范围。因此，通过这项研究工作发展起来的理论应该成为弹性领域基础知识体系的新补充。这项研究还将包括通过招收本科生和研究生来支持教育，并增加工程专业学生和公众对具有微观结构的革命性材料的接触。均衡晶格表现出许多无限小的坍塌机制，即零模态，这些机制对预设的几何扭曲（如Kagome晶格中的扭曲）很敏感。在拓扑跃迁中，零模式从均匀分布在块和边上转变为过度填充优先边。在这种情况下，等静力晶格表现出极化行为，它在一边显得柔软，而在另一边显得坚硬。本项目的主要目的是了解极化在宏观尺度上产生和消退的微观结构机制。重点是极化效应，即使当单元格的尺寸与整个晶格相比变得无穷小时，极化效应仍然占主导地位。研究工作围绕两个目标进行：(1)建立一个运动学丰富的弹性连续体理论，称为？microtwist弹性?，通过适当发展的渐近均质化方法，能够定量和定性地模拟极化效应以及底层零模；(2)研究微扭理论预测的静态和动态现象的范围，并通过制造样品的力学测试系统地验证这些预测。提出的理论应该带来一个基本的新的理解与基于等静力晶格的微结构的建筑材料。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Lattice-based metamaterials are materials that have a defined architecture reminiscent of atomic lattices but at a larger length scale. These materials oftentimes display unique capabilities that can be traced back to their micro-architected design. Modern advances in fabrication techniques together with increasingly environmentally conscious design constraints have motivated research in lattice-based mechanical metamaterials, which offer a range of properties unusual to natural materials. To enable their use, it is mandatory to build a fine understanding of how the composition, geometry and overall morphology of the underlying truss govern the mechanical properties desired and targeted on the macroscopic scale (centimeter to meter). This proposal aims to design, model and test lattice metamaterials that are polarized: while featuring the same microstructure everywhere, they still manage to be soft to indentation on one side but hard on the opposite side. While electric polarization is a classical concept of continuum electrodynamics, mechanical polarization in elastostatics and elastodynamics has escaped the scope of earlier theories. The theory developed through this research effort should thus be a new addition to the body of fundamental knowledge in the field of elasticity. The research will also include support of education through recruiting undergraduate in research and graduate students and increasing exposure of engineering students, and the general public, to revolutionary materials with microstructure.Isostatic lattices exhibit a number of infinitesimal collapse mechanisms, i.e., zero modes, that are sensitive to pre-set geometric distortions, such as twisting in Kagome lattices. In a topological transition, zero modes shift from being evenly distributed across bulk and edges to overpopulate preferential edges. In that case, the isostatic lattice displays a polarized behavior where it appears soft on one side and hard on the opposite side. The main aim of the present project is to understand the microstructural mechanisms by which polarization emerges and fades on a macroscopic scale. Focus is on polarization effects that remain dominant even when the size of the unit cell becomes infinitesimal in comparison to the whole lattice. Research efforts are structured around two goals: (1) to build a kinematically enriched continuum theory of elasticity, called ?microtwist elasticity?, capable of modeling polarization effects as well as the underlying zero modes quantitatively and qualitatively by employing suitably developed asymptotic homogenization methods; (2) to investigate the range of static and dynamic phenomena predicted by the microtwist theory and to systematically validate these predictions by mechanical testing of fabricated samples. The proposed theory should bring a fundamental new understanding of architected materials with microstructures based on isostatic lattices.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.