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

长期以来，科学界一直对软质水合材料的力学性能感兴趣。软材料由于其设计的灵活性和有意利用非线性等明显的优点，在机械设计中的应用日益突出。特别是软质材料的高速率响应，由于其在机器人、材料和生物医学等领域的广泛应用而受到人们的关注。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，由于测量不确定性、力学各向异性和不均匀性，难以量化。在本项目中，将制定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和模拟软水合材料。这项研究的发现有可能大大提高宽带软材料表征的准确性、成本效益和可及性，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期间的软组织反馈。由此产生的软材料模型更新方法将在预测工程设计中具有变革性，因为它将使软材料在各种应用中得到更好的利用和集成。该方法既可用于软机械设计的非线性分析，也可用于软机械设计的健康监测。该项目还将为K12、本科生和研究生等不同群体提供培训和指导机会，特别强调代表性不足的群体。计划在本地科学节以互动方式展示所开发的方法，以吸引公众对这一科学问题的兴趣。本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水合材料。它基于对测量响应时间序列的直接分析，以及在软组织测试仪和样品系统的适当定义的频率-能量图（fep）中构建适当定义的跃迁。然后，通过计算非线性正态模态（NNMs），将为测试器建模的潜在保守系统（即没有耗散效应的相应系统）的动力学与测量响应相关联。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fep中测量和模拟响应的调和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。本研究中基于物理的非线性方法用于模型更新是前所未有的，因为它完全基于直接时间序列分析，并且框架足够通用，可以适用于其他工程应用，例如非线性有限元模型与实验测量的调和，以及机械和航空航天部件的精确模型缩减。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的动力转换和模态相互作用的理解。它还将使此类系统的预测工程设计成为可能，并将通过开发和应用独特的基于非线性动力学的新模型更新框架，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.