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

现代材料科学的进步表明，软有机固体——例如电活性和磁活性弹性体、凝胶和形状记忆聚合物——在实现新的高端技术方面具有巨大的潜力，特别是作为下一代传感器和执行器，它们具有低成本、生物相容性、可加工成任意形状以及承受大的可逆变形的独特能力。这种潜力的实现引发了软材料计算微观和介观研究的热潮，其目标是自下而上定量地了解它们的行为，并最终指导它们的优化和在技术应用中的实际使用。几乎所有这些研究都使用了标准有限元，但事实证明这些标准无法模拟涉及实际大变形的过程。参与该项目的研究生将受益于该研究的协作计算/理论特征。这项跨学科研究开发的概念将被纳入课程中，并对工程教育产生积极影响。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。第二个目标是部署该技术来研究具有复杂颗粒微结构（例如用各向异性填料颗粒增强的弹性体）的软固体的非线性弹性响应，这种结构在许多软活性材料系统中普遍存在。从概念的角度来看，这将通过利用模仿启发的方法（保留物理和数学模型的基本属性，从而提高计算机模拟的预测能力）来实现，在有限元和虚拟元素方法的背景下，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.