Characterization and Simulation of Dispersive Elastodynamic Media in Time Domain

许多材料是色散的，也就是说，它们的性质与频率有关。波与材料微观结构的相互作用会导致复杂的色散响应。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。该奖项支持对弹性动力分散材料的表征和分析的基础研究，作为其机械布局和微观尺度上的无序水平的函数。了解分散材料的反应对国家繁荣和福利以及国防的广泛应用具有重要意义。例如，弹性动力超材料可以应用于地震波减缓、振动控制和爆炸波减缓。此外，许多天然和人造分散材料的微观结构是固有的。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减波特性，促进非破坏性评估和能量收集应用的新设计。该奖项还将通过与主要的本科院校、研究生研究和课程开发以及公开共享的软件模块合作，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质化方法，该方法推导出分散材料的动态特性，然后采用数值方法将这些特性纳入瞬态分析。均匀化性质一般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用于扩展这一点，并推导出有效的动态特性，这些特性在中短波长范围内都是有意义的。由此产生的有效性质可能相当复杂，例如，通过具有张量质量密度并产生威利斯本构方程。在时域中对色散关系进行建模带来了额外的挑战。将制定一种自动化方法来推导复杂的辅助微分方程，以便在时域内进行分析。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。具体来说，无序可以通过扩大阻带的频率范围，使吸收更加全向，以及红移阻带来增强超材料设计的减波特性，这通常是一种受欢迎的效果。统计分析将用于分析阻带和其他动态特性对无序的灵敏度和稳定性。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。

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.