Polygonal and Polyhedral Elements as a New Computational Paradigm to Study Soft Materials

材料科学的现代进展表明，软有机固体--如电磁和磁活性弹性体、凝胶和形状记忆聚合物--具有实现新的高端技术的巨大潜力，特别是作为新一代传感器和执行器，其特点是低成本，以及它们的生物兼容性、可加工成任意形状以及经历大的可逆变形的独特能力。这种潜力的实现推动了软材料的计算微观和介观研究的热潮，目的是自下而上地定量了解它们的行为，并最终指导它们在技术应用中的优化和实际使用。几乎所有这些研究都使用了标准的有限元，这些有限元一再被证明无法模拟涉及实际大变形的过程。参与该项目的研究生将从该研究的协作计算/理论特征中受益。从这项跨学科研究中发展出的概念将被应用到课程中，并将对工程教育产生积极的影响。该项目的主要目标是提出一种新的计算技术，能够研究经历实际大变形的软固体。第二个目标是利用这项技术来研究具有复杂颗粒微结构的软固体(例如，各向异性填充颗粒增强的弹性体)的非线性弹性响应，这些弹性体普遍存在于许多软活性材料体系中。从概念上看，这将通过利用模拟启发方法(保留物理和数学模型的基本性质，从而提高计算机模拟的预测能力)来实现，以在有限元和虚拟元方法的背景下提出一种新的有限变形下任意形状单元的离散化方法。这项工作涉及与米兰大学和洛斯阿拉莫斯国家实验室的合作。

Modern advances in materials science have revealed that soft organic solids --- such as electro- and magneto-active elastomers, gels, and shape-memory polymers --- hold tremendous potential to enable new high-end technologies, especially as the next generation of sensors and actuators featured by their low cost together with their biocompatibility, processability into arbitrary shapes, and unique capability to undergo large reversible deformations. The realization of this potential has prompted an upsurge in the computational microscopic and mesoscopic studies of soft materials with the objectives of quantitatively understanding their behavior from the bottom up and ultimately guiding their optimization and actual use in technological applications. Almost all of these studies have made use of standard finite elements, which have repeatedly proved unable to simulate processes involving realistically large deformations. The graduate students involved in the project will benefit from the collaborative computational/theoretical character of the research. Concepts developed from this interdisciplinary research will be adapted into the curriculum and will positively impact engineering education.The main objective of this project is to put forward a new computational technology with the capability to study soft solids undergoing realistically large deformations. A second objective is to deploy this technology to study the nonlinear elastic response of soft solids with complex particulate microstructures (e.g. elastomers reinforced with anisotropic filler particles), ubiquitous in many soft active material systems. From a conceptual point of view, this will be accomplished by making use of mimetic inspired methods (which preserve the underlying properties of physical and mathematical models, thereby improving the predictive capability of computer simulations) to put forward a new discretization approach for arbitrarily shaped elements under finite deformations in the context of finite element and virtual element methods. This work involves collaboration with the University of Milan and Los Alamos National Laboratory.