Finite Element Approximations of Bending Actuated Devices

从相对较小的能量产生复杂变形的能力在微工程和生物医学科学中有着巨大的应用。这项研究的重点是开发和实施能够预测和优化弹性薄膜变形的数学算法，选择弹性薄膜是因为它们在生产坚固和轻量微尺度设备方面的潜力。考虑的变形是由于暴露在外部刺激下而触发的，这些外部刺激要么是具有不同膨胀特性的聚合物，要么是具有残余应力的人造凝胶。例如，基于这些技术的设备被用作药物输送囊泡、细胞封装设备、传感器、生物肌肉和组织生长的替代品。除了在生物医学科学中的这些应用外，自主可折叠结构的发展，如航天器或可展开飞行器中的自展开太阳帆、光伏设备、致动器、微型马达、微型抓取器、微阀、微型游泳器等，都是工程界非常感兴趣的研究课题。拟议中的研究集中在弯曲是导致可能大变形的主要机制的薄装置上。建立了三维超弹性薄体的二维极限的数学模型。它们的特征是以弯曲为主的能量密度，几何上表示为薄膜的第二基本形式。除了这种四阶系统的无散度形式所固有的困难之外，在大变形的情况下还必须考虑完全非线性的几何约束。这项研究的目的是在不适用于目标应用的情况下推导出数学模型，并设计、分析和实现基于有限元的算法来逼近它们。覆盖了从数学分析到有限元算法的实际高度并行实现的整个过程。因此，从微分几何和变分中借用的分析工具与数值分析和精细的计算工作相结合，以实现高效和实用的算法。从相对较小的能量产生复杂变形的能力在微工程和生物医学科学中有着巨大的应用。由拟议的研究产生的算法--特别是其相对轻松的实现--可能会在这些领域产生影响。举几个例子，基于双层聚合物或预张紧膜的装置被用作药物输送微囊、细胞封装装置、传感器、生物肌肉和作为组织生长的替代品。除了在生物医学科学中的这些应用，自主可折叠结构的开发，如航天器或可展开飞机上的自展开太阳帆、光伏设备、工程脚手架、执行器、微型马达、微型抓取器、微阀、微型游泳者都是工程界非常热门的研究兴趣。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The ability to generate complex deformations from relatively small energies has tremendous applications in micro-engineering and biomedical science. This research focuses on developing and implementing mathematical algorithms able to predict and optimize the deformation of elastic films, chosen for their potential in the production of robust and light-weight micro-scale devices. The deformations considered are triggered by exposing to external stimuli either polymers with different expansion characteristics or manufactured gels with residual stresses. Devices based on these technologies are, for instance, employed as drug delivery vesicles, cell encapsulation devices, sensors, bio-muscles and as proxies for tissue growth. In addition to these applications in biomedical science, the development of autonomous foldable structures such as self-deployable sun sails in spacecraft or deployable aircrafts, photovoltaic devices, actuators, micromotors, microgrippers, microvalves, microswimmers are very popular interests in the engineering community this research is likely to have impact on.The proposed study focuses on thin devices where bending is the principal mechanism for, possibly large, deformations. The mathematical models are derived as the two dimensional limit of thin three dimensional hyper-elastic solids. They are characterized by energy densities dominated by bending, expressed geometrically as the film's second fundamental form. In addition to the difficulties inherent in the non-divergence form of this fourth order system, fully non-linear geometrical constraints must be taken into account in the context of large deformations. The aim of this research is to derive mathematical models when not available for the targeted application, and to design, analyze and implement finite element based algorithms for their approximations. The entire process from the mathematical analysis to the actual highly parallel implementation of finite element algorithms is covered. Hence, analytical tools borrowed from differential geometry and calculus of variation are blended with numerical analysis and delicate computational efforts to achieve efficient and practical algorithms. The ability to generate complex deformations from relatively small energies has tremendous application in micro-engineering and biomedical science. The algorithms resulting from the proposed research - and in particular their relatively effortless implementations - are likely to have impact in these areas. To mention a few applications, devices based on bilayers of polymers or prestrained films are employed as drug delivery vesicles, cell encapsulation devices, sensors, bio-muscles and as proxies for tissue growth. In addition to these applications in biomedical science, the development of autonomous foldable structures such as self-deployable sun sails in spacecraft or deployable aircrafts, photovoltaic devices, engineered scaffolds, actuators, micromotors, microgrippers, microvalves, microswimmers are very popular research interests in the engineering community.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.