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数学算法，能够预测和优化弹性薄膜的变形，选择它们在生产强大和重量轻的微型设备的潜力。所考虑的变形是由暴露于外部刺激，具有不同的膨胀特性的聚合物或制造的凝胶与残余应力。例如，基于这些技术的装置被用作药物递送囊泡、细胞封装装置、传感器、生物肌肉和作为组织生长的替代物。 除了在生物医学科学中的这些应用之外，自主可折叠结构的开发，例如航天器或可展开飞机中的自展开太阳帆，光伏器件，致动器，微电机，微夹，微阀，微游泳者，在工程界非常受欢迎，这项研究可能会产生影响。可能是大的变形。 数学模型推导为薄的三维超弹性固体的二维极限。它们的特点是能量密度主要由弯曲，表示为几何薄膜的第二基本形式。除了该四阶系统的非发散形式中固有的困难之外，在大变形的情况下必须考虑完全非线性的几何约束。本研究的目的是推导出数学模型时，不适用于目标应用程序，并设计，分析和实施有限元算法的近似。涵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，从微分几何和变分学借用的分析工具与数值分析和精细的计算工作相结合，以实现有效和实用的算法。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具有巨大的应用。从拟议的研究中产生的算法-特别是它们相对轻松的实现-可能会在这些领域产生影响。举几个应用，基于双层聚合物或预应变膜的装置被用作药物递送囊泡、细胞封装装置、传感器、生物肌肉和作为组织生长的替代物。除了在生物医学科学中的这些应用之外，自主可折叠结构的发展，例如航天器或可展开飞行器中的可自展开太阳帆、光伏器件、工程支架、致动器、微电机、微夹持器、微阀、微型游泳者是工程界非常受欢迎的研究兴趣。该奖项反映了NSF的法定使命，并通过使用基金会的学术价值和更广泛的影响审查标准。

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.