Characterization and Simulation of Dispersive Elastodynamic Media in Time Domain

许多材料是色散的，也就是说，它们的性质是频率相关的。波与材料微观结构的相互作用会导致复杂的频散响应。这种效应在超材料的设计中被利用，以实现在传统材料中没有观察到的新特性。该奖项支持关于弹性动力弥散材料的表征和分析的基础研究，这些研究是其在微观尺度上的机械布局和无序程度的函数。了解分散材料的响应对于广泛应用于国家繁荣福利和国防具有重要意义。例如，弹性动力学超材料在地震波缓解、振动控制和爆炸波缓解方面得到了应用。此外，许多天然和人造分散材料的微观结构中都存在无序现象。对于超材料来说，由于制造缺陷，无序是不可避免的，但这种必然性可以用来改善波的抑制性能，促进用于无损评估和能量收集应用的新设计。该奖项还将通过与以本科生为主的机构合作、研究生研究和课程开发以及公开共享的软件模块来支持学生实习和教师研究机会。该项目的第一个目标是制定先进的均化方法，得出分散材料的动态特性，然后是结合这些特性进行瞬变分析的数值方法。均一化性质通常只在准静态到长波长范围内有效。高阶散射系数和空间色散项将被用来扩展这一点，并推导出直到中到短波长区域都有意义的有效的动力学性质。由此产生的有效性质可能非常复杂，例如，通过具有张量质量密度并导致Willis本构方程。在时间域中对离散关系进行建模带来了额外的挑战。将制定一种自动方法来推导复杂的辅助微分方程组，以便在时间域中进行分析。第二个目标是了解无序对分散材料的各种响应措施的影响。具体地说，无序可以通过扩大阻带的频率范围(S)、使吸收更加全方位以及红移阻带来增强超材料设计的减波性能，这通常是一种受欢迎的效果。统计分析将被用来分析阻带和其他动态特性相对于无序的敏感性和稳定性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Many materials are dispersive, i.e., their properties are frequency-dependent. The interaction of waves with material microstructure can result in a complex dispersive response. This effect is exploited in the design of metamaterials to effectuate novel properties that are otherwise not observed in conventional materials. This award supports fundamental research on the characterization and analysis of elastodynamic dispersive materials as a function of their mechanical layout and level of disorder at the microscale. Understanding the response of dispersive materials is important for a broad range of applications towards national prosperity and welfare and the national defense. For example, elastodynamic metamaterials find applications in seismic wave mitigation, vibration control, and blast wave mitigation. Moreover, disorder is inherent in the microstructure of many natural and man-made dispersive materials. For metamaterials, disorder is unavoidable due to manufacturing imperfections, but this inevitability can be used to improve wave mitigation properties and facilitate novel designs for non-destructive evaluation and energy harvesting applications. This award will also support student internship and faculty research opportunities through collaboration with a predominantly undergraduate institution, graduate research and course development, and publicly shared software modules.The first objective of this project is the formulation of advanced homogenization methods that derive dynamic properties of dispersive materials followed by numerical methods that incorporate such properties for transient analysis. Homogenized properties are generally valid only from quasi-static to long wavelength regimes. Higher order scattering coefficients and spatial dispersion terms will be used to extend this and derive effective dynamic properties that are meaningful up to medium to short wavelength regimes. The resulting effective properties can be quite complex, for example, by having a tensorial mass density and resulting in Willis constitutive equations. Modeling dispersive relations in time domain poses additional challenges. An automated method will be formulated to derive complex auxiliary differential equations for analysis in the time domain. The second objective is understanding the effect of disorder on various response measures of dispersive materials. Specifically, disorder can enhance wave mitigation properties of a metamaterial design by expanding the frequency range of the stopband(s), making the absorption more omnidirectional, and red-shifting the stopband which is often a welcomed effect. Statistical analysis will be used to analyze the sensitivity and stability of stopband and other dynamic properties versus disorder.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.