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

该奖项支持的基础研究导致了一类新的机械超材料，与传统材料不同，这种材料对载荷的细微空间波动的反应比对粗糙载荷的反应更强。超材料的概念是指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特别设计的相互作用导致在天然材料中观察到的某些基本性质的逆转。这些新特性揭示了对社会非常有益的实际机会。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。它们还可能使结构和建筑基础的不安全加载条件的现场识别成为可能。这项工作的范式改变方面将有助于激励本科生和未被充分代表的群体通过本科生的研究经历和在ASEE工程教育杂志上提交手稿参与研究活动。这项研究将为这些新型超材料的设计和制造创造足够的知识基础。在离散非局部弹性介质傅里叶域传递矩阵特征分析的基础上，引入了变形衰减谱的概念。基于衰减谱和态密度分析，相图将在有趣的候选结构的设计空间中构建，以显示适合实际超材料的结构参数组合。衰减谱中渐近带隙的可用性将表明对于给定的非局部介质可以实现超材料行为。在数学上，这些带隙将需要复数衰减参数，作为非局部介质平衡控制方程基本解中的傅里叶模式指数的非线性函数。一个复杂的衰减参数将指出材料中静态傅里叶模式行为的某些异常，包括相移和反转，以及伴随着圣维南边缘效应反转的表面模式阻塞。这些基本现象将显示为静态变形遮蔽、过滤和反转创造机会。更广泛地说，它们将导致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.