Collaborative Research: A New Nonlinear Modal Updating Framework for Soft, Hydrated Materials

长期以来，软质、水合材料的机械性能一直受到科学界的关注。软材料在机械设计中的应用因其在设计上的灵活性和对非线性的有意利用等明显优势而日益突出。尤其是软材料由于其在机器人、材料和生物医学等领域的广泛应用，其高响应速度引起了人们的广泛关注。由于测量的不确定性、力学各向异性和非均质性，大多数软质和水合材料(如生物材料)表现出复杂的力学行为，难以量化。在这个项目中，将制定一种新的基于非线性动力学的系统辨识和模型修正方法来表征和模拟软的、水合的材料。这项研究的结果有可能极大地提高宽带软材料表征的准确性、成本效益和可获得性，因此，它可以在不同的跨学科领域产生变革，例如软机器人设计、机械压痕测量和手术中的软组织反馈。由此产生的软材料模型修正方法将在预测性工程设计中具有变革性，因为它将使软材料在不同应用中更好地利用和集成。这种方法既可用于开发软机械设计中的非线性，也可用于其健康监测。该项目还将为不同的K12、本科生和研究生群体提供培训和指导机会，特别强调代表性不足的群体。这个项目的主要目标是引入一种新的基于非线性动力学的系统识别和模型更新方法来表征软的、水合的材料。它基于对测量的响应时间序列的直接分析，并在软组织测试仪和样本系统的适当定义的频率-能量图(FEP)中构建适当定义的转变。然后，通过计算非线性简正模式(NNM)，将模拟测试仪的基本保守系统(即，没有耗散效应的相应系统)的动力学与测量的响应相关联。在保守系统模型中，软组织被建模为具有刚度和阻尼非线性的高度柔性单元。然后，利用FEPS中测量和模拟的响应的一致性来估计软组织的宽带耗散特性。实验验证将通过测试软材料，如肌腱、水合PDMS和脑组织来完成。这项研究中基于物理的非线性模型修正方法是前所未有的，因为它完全基于直接的时间序列分析，而且该框架具有足够的通用性，可以应用于其他工程应用，如非线性有限元模型与实验测量的协调，以及机械和航空航天部件的精确模型降阶。此外，这项研究将极大地加深我们对具有非线性粘弹性系统中复杂的动力学转变和模式相互作用的理解。它还将使此类系统的预测性工程设计成为可能，并将通过开发和应用一种独特的基于非线性动力学的模型修正框架，为软材料的宽带响应提供新的见解。

The mechanical properties of soft, hydrated materials have long been of interest to the scientific community. Using soft materials in mechanical designs is becoming increasingly prominent due to their obvious advantages such as flexibility in design and intentional exploitation of nonlinearity. Especially, the high-rate response of soft materials has received attention due to their many applications in robotics, materials and the biomedical sciences. Most soft and hydrated materials (e.g., biomaterials) exhibit complex mechanical behavior that is challenging to quantify due to measurement uncertainties, mechanical anisotropy and inhomogeneity. In this project, a new nonlinear dynamics-based system identification and model updating methodology will be formulated to characterize and model soft, hydrated materials. The findings of this research have the potential to drastically enhance the accuracy, cost-efficiency and accessibility of broadband soft material characterization, and, as such, it can be transformative in diverse interdisciplinary areas, such as soft robotic design, mechanical indentation measurements and soft tissue feedback during surgery. The resulting model updating approach for soft materials will be transformative in predictive engineering designs since it will enable the better utilization and integration of soft materials in diverse applications. This approach can be used for both exploiting the nonlinearities in soft mechanical designs, as well as for their health monitoring. This project will also provide training and mentoring opportunities for a diverse group of K12, undergraduate and graduate students, with a special emphasis on underrepresented groups. Interactive demonstrations of the developed methodology are planned to be displayed in local science festivals to engage the interest of the public in this scientific issue.The main objective of this project is to introduce a new nonlinear dynamics-based system identification and model updating methodology to characterize soft, hydrated materials. It is based on direct analysis of measured response time series, and construction of appropriately defined transitions in appropriately defined frequency-energy plots (FEPs) of a soft-tissue tester and sample system. The dynamics of an underlying conservative system (i.e., the corresponding system with no dissipative effects) modeling the tester is then correlated with the measured response by computing nonlinear normal modes (NNMs). In the conservative system model, soft tissues are modeled as highly flexible elements with stiffness and damping nonlinearities. Then, the reconciliation of the measured and simulated responses in the FEPs is utilized to estimate the broadband dissipative properties of the soft tissues. The experimental validation will be done by testing soft materials such as tendons, hydrated PDMS and brain tissue. The physics-based nonlinear approach in this study for model updating is unprecedented since it is based exclusively on direct time series analysis, and the framework is sufficiently general to be applicable to other engineering applications, such as the reconciliation of nonlinear finite element models with experimental measurements, and the accurate model reduction of mechanical and aerospace components. Moreover, this research will drastically increase our understanding of complicated dynamical transitions and modal interactions in systems with nonlinear viscoelastic properties. It will also enable predictive engineering design of such systems and will provide new insights into the broadband response of soft materials by developing and applying a uniquely new nonlinear-dynamics based model updating framework.