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

长期以来，科学界一直对柔软的水合材料的机械性能感兴趣。软材料以其设计灵活、可有意利用非线性等优点，在机械设计中的应用日益突出。特别是，由于软材料在机器人、材料和生物医学科学中的许多应用，其高速率响应受到关注。大多数柔软和水合的材料（例如，生物材料）表现出复杂的机械行为，由于测量不确定性、机械各向异性和不均匀性，该机械行为难以量化。在这个项目中，一个新的非线性动力学为基础的系统识别和模型更新方法将制定的特点和模型软，水合材料。这项研究的结果有可能大大提高宽带软材料表征的准确性，成本效益和可访问性，因此，它可以在不同的跨学科领域进行变革，例如软机器人设计，机械压痕测量和手术过程中的软组织反馈。由此产生的软材料模型更新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得到更好的利用和集成。这种方法可用于利用软机械设计中的非线性，以及用于其健康监测。该项目还将为K12，本科生和研究生的多样化群体提供培训和指导机会，特别强调代表性不足的群体。计划在当地的科学节上展示所开发方法的互动演示，以吸引公众对这一科学问题的兴趣。该项目的主要目标是介绍一种新的基于非线性动力学的系统识别和模型更新方法，以表征柔软的水合材料。它是基于测量的响应时间序列的直接分析，并在适当定义的频率能量图（FEP）的软组织测试仪和样品系统的适当定义的过渡的建设。一个潜在的保守系统的动力学（即，没有耗散效应的相应系统），然后通过计算非线性简正模（NNM）将模拟测试器的响应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元件。然后，利用有限元法中的测量和模拟响应的调和来估计软组织的宽带耗散特性。将通过测试软材料（如肌腱、水合PDMS和脑组织）进行实验验证。在这项研究中，基于物理的非线性模型更新方法是前所未有的，因为它是完全基于直接的时间序列分析，和框架是足够的一般适用于其他工程应用，如非线性有限元模型与实验测量的和解，以及精确的模型减少机械和航空航天部件。此外，这项研究将大大增加我们对非线性粘弹性系统中复杂动力学转变和模态相互作用的理解。它还将实现此类系统的预测性工程设计，并通过开发和应用一种独特的新的基于非线性动力学的模型更新框架，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.