Structural Metamaterials with Saint-Venant Edge Effect Reversal for Static Load Pattern Modification and Recognition

该奖项支持基础研究，导致了一类新的机械超材料，与传统材料不同，这种材料对载荷中更精细的空间波动的响应比对更粗糙的空间波动更强。超材料的概念指的是一类具有工程内部结构的令人兴奋的材料系统。内部结构的各个元素之间经过特殊设计的相互作用导致了在天然材料中观察到的某些基本性质的逆转。这些新的物业揭示了可能对社会非常有益的实践机会。例如，光子超材料可用于制造医疗应用的超薄透镜，声学超材料可提供高效的隔音和地震减灾系统。它们还可能使现场识别结构和建筑基础中的不安全载荷条件。这项工作的范式转变方面将有助于通过本科生的研究经验和在ASEE工程教育杂志上提交手稿来激励本科生和代表性不足的群体参与研究活动。这项研究将创造足够的知识基础，使这些新型超材料的设计和制造成为可能。基于离散非局部弹性介质在富里叶域的传递矩阵特征分析，引入了变形衰减谱的概念。基于衰减谱和态密度的分析，将在感兴趣的候选结构的设计空间中构建相图，以显示什么结构参数组合适合于实际的超材料。衰减谱中渐近带隙的可用性将表明，对于给定的非局域介质，超材料行为是可以实现的。在数学上，这些带隙将需要复值衰减参数，作为非局域介质平衡控制方程的基本解中的傅立叶模折射率的非线性函数。一个复杂的衰减参数将指出材料中静态傅立叶模式行为的某些反常现象，包括相移和反转，以及伴随圣维南边缘效应反转的表面模式阻塞。这些基本现象将被展示为静态变形伪装、过滤和反转创造机会。更广泛地说，它们将导致用于定性修饰和识别表面负载模式的功能超材料。

This award supports fundamental research leading to a new class of mechanical metamaterials that, unlike the traditional materials, respond stronger to finer spatial fluctuations in loads than to coarser ones. The notion of metamaterials refers to an exciting class of material systems with engineered internal structure. Specially designed interactions among individual elements of the internal structure lead to a reversal of certain basic properties observed in natural materials. These new properties unveil practical opportunities that can be highly beneficial to the society. For example, photonic metamaterials may be used to fabricate ultrathin lenses for medical applications, and acoustic metamaterials can provide highly efficient sound insulation and earthquake hazard mitigation systems. They will also potentially enable in-situ identification of unsafe loading conditions in structures and building foundations. The paradigm changing aspects of this work will help to inspire undergraduate students and underrepresented groups to participate in the research activities through undergraduate research experiences and the submission of manuscripts in the ASEE Journal of Engineering Education. This research will create a sufficient base of knowledge to enable design and fabrication of these novel metamaterials. The concept of deformation decay spectrum will be introduced on the basis of transfer matrix eigenanalysis of a discrete nonlocal elastic medium in the Fourier domain. Based on the decay spectrum and density of states analyses, phase diagrams will be constructed in the design space of interesting candidate structures to show what combinations of structural parameters are suitable for an actual metamaterial. Availability of asymptotic bandgaps in the decay spectrum will indicate that the metamaterial behavior is achievable for a given nonlocal medium. Mathematically, these bandgaps will require complex-valued decay parameters, as a nonlinear function of the Fourier mode index in a fundamental solution to the governing equation of equilibrium of the nonlocal medium. A complex decay parameter will point out on certain anomalies in the behavior of static Fourier modes in the material, including phase shift and inversion, and mode blockage at surfaces accompanied by the Saint-Venant edge effect reversal. These basic phenomena will be shown to create opportunities for static deformation cloaking, filtering and inversion. More broadly, they will lead to functional metamaterials for qualitative modification and recognition of surface load patterns.