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

协作研究：用于软水合材料的新型非线性模态更新框架

• 批准号: 1727761
• 负责人: Alexander Vakakis
• 金额: $ 25.93万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1727761&HistoricalAwards=false
• 关键词: Collaborative; Research; New; Nonlinear; Modal

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.

柔软的水合材料的机械性能长期以来一直引起科学界的兴趣。由于其明显的优势，例如设计灵活性和有意利用非线性，在机械设计中使用软材料变得越来越重要。特别是软材料的高速率响应因其在机器人、材料和生物医学领域的广泛应用而受到关注。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，由于测量的不确定性、机械各向异性和不均匀性而难以量化。在该项目中，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柔软的水合材料。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产生变革，例如软机器人设计、机械压痕测量和软体材料表征。手术期间的组织反馈。由此产生的软材料模型更新方法将在预测工程设计中带来变革，因为它将能够在不同的应用中更好地利用和集成软材料。这种方法可用于利用软机械设计中的非线性及其健康状况监测。该项目还将为 K12、本科生和研究生等多元化群体提供培训和指导机会，特别关注代表性不足的群体。计划在当地科学节上展示所开发方法的交互式演示，以引起公众对这一科学问题的兴趣。该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柔软、水合的材料。它基于对测量的响应时间序列的直接分析，以及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态 (NNM)，将测试仪建模的基础保守系统（即没有耗散效应的相应系统）的动态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灵活的元素。然后，利用 FEP 中测量响应和模拟响应的协调来估计软组织的宽带耗散特性。实验验证将通过测试肌腱、水合聚二甲基硅氧烷和脑组织等软材料来完成。本研究中用于模型更新的基于物理的非线性方法是前所未有的，因为它完全基于直接时间序列分析，并且该框架足够通用，可适用于其他工程应用，例如非线性有限元模型与实验的协调测量以及机械和航空航天部件的精确模型还原。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态转变和模态相互作用的理解。它还将实现此类系统的预测工程设计，并通过开发和应用基于非线性动力学的独特的新型模型更新框架，为软材料的宽带响应提供新的见解。

项目成果

Strong geometric softening–hardening nonlinearities in an oscillator composed of linear stiffness and damping elements

• DOI: 10.1016/j.ijnonlinmec.2018.09.004
• 发表时间: 2018-12
• 期刊: International Journal of Non-Linear Mechanics
• 影响因子: 3.2
• 作者: A. Mojahed;K. Moore;L. Bergman;A. Vakakis

Modal energy exchanges in an impulsively loaded beam with a geometrically nonlinear boundary condition: computation and experiment

具有几何非线性边界条件的脉冲加载梁中的模态能量交换：计算和实验

• DOI: 10.1007/s11071-020-06156-7
• 发表时间: 2021
• 期刊: Nonlinear Dynamics
• 影响因子: 5.6
• 作者: Mojahed, Alireza;Liu, Yang;Bergman, Lawrence A.;Vakakis, Alexander F.
• 通讯作者: Vakakis, Alexander F.

A Nonlinear Reduced-Order Model of the Corpus Callosum Under Planar Coronal Excitation

平面冠状激励下胼胝体的非线性降阶模型

• DOI: 10.1115/1.4046503
• 发表时间: 2020
• 期刊: Journal of Biomechanical Engineering
• 作者: Mojahed, Alireza;Abderezaei, Javid;Kurt, Mehmet;Bergman, Lawrence A.;Vakakis, Alexander F.
• 通讯作者: Vakakis, Alexander F.

New inverse wavelet transform method with broad application in dynamics

• DOI: 10.1016/j.ymssp.2021.107691
• 发表时间: 2021-02-06
• 期刊: MECHANICAL SYSTEMS AND SIGNAL PROCESSING
• 影响因子: 8.4
• 作者: Mojahed, Alireza;Bergman, Lawrence A.;Vakakis, Alexander F.
• 通讯作者: Vakakis, Alexander F.