CDS&E: Multiscale Computational Modeling of Flow-Induced Mechanical Deformation via Nonlocal Formulations

这个计算和数据驱动的科学与工程（CDS&amp；E）项目将通过实现与生物医学相关的复杂机械问题的预测模拟（如何在手术后将组织层粘附在一起）和涂层和密封剂的开发（如何确保干燥的油漆仍然附着在表面上），为国家繁荣和经济福利的进步做出贡献。大多数人都经历过这样的挑战：从表面撕下一块胶带，或者试图抬起粘在湿玻璃桌面上的薄物体。从油漆和diy家庭维修到尿布和卫生用品，软涂层涉及到流体层介导的弹性材料与刚性基材的粘附。在现实场景中，准确模拟粘合和脱粘过程（包括材料失效）的能力仍然是一个挑战。该基金支持的基础研究将通过发展理论来促进科学进步，这些理论将导致能够处理流体薄层和柔软弹性表面之间复杂相互作用的快速准确的模拟工具，这些表面可以粘附、分离，甚至由于流体流动而撕裂。本科生和研究生将接受计算力学方面的培训，与HBCU的计划互动将增加追求更高学位的个人的多样性，并最终增加STEM劳动力的多样性。通过构建可处理的一维模型，耦合流体流动的非局部力学响应，该资助将能够使用连续介质力学的非局部公式进行流致机械变形的预测、多尺度模拟，从而创建周动力学方程的3D求解器，采用新颖的有限体积离散化方法，允许模拟具有非局部力学特征的双向耦合流固相互作用。利用数学分析的最新发展，例如用于定义拉普拉斯非局部泛化的弱奇异核，将推导出非局部一维模型，以理解纳米片流动驱动分层的基本原理，而经典连续介质力学方法无法实现。来自无网格（粒子）方法的有限体积实现的想法将用于在标准化的开源框架上设计和构建3D计算工具，这些框架可以免费提供给研究人员和从业者。由此产生的计算工具将能够桥接尺度（通过非局部理论从中尺度到连续尺度），以实现与软粘附、增材制造和生物物理学等应用相关的非局部力学耦合的流动预测模拟。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This Computational and Data-Enabled Science and Engineering (CDS&E) project will contribute to the advancement of national prosperity and economic welfare by enabling predictive simulations of complex mechanical problems with relevance to biomedicine (how to adhere layers of tissue together after surgery) and the development of coatings and sealants (how to ensure dried paint remains attached to a surface). Most have experienced the commonplace challenge of peeling off a piece of tape from a surface or attempting to lift a thin object stuck to a wet glass tabletop. From paint and do-it-yourself home repair to diapers and hygiene products, soft coatings involve the fluid-layer-mediated adhesion of an elastic material to a rigid substrate. The ability to accurately simulate the adhesion and debonding processes, including material failure, in real-world scenarios remains a challenge. The fundamental research supported by this grant will promote the progress of science by developing theories that will lead to fast and accurate simulation tools capable of handling the complex interaction between thin layers of fluids and soft, elastic surfaces that can adhere, detach, or even tear apart due to the flow of the fluid. Undergraduate and graduate students will be trained in computational mechanics, and planned interactions with an HBCU will increase the diversity of individuals pursuing higher degrees, and ultimately of the STEM workforce.This grant will enable predictive, multiscale simulation of flow-induced mechanical deformation using nonlocal formulations of continuum mechanics via the construction of tractable 1D models coupling nonlocal mechanical response to fluid flow, leading to creation of 3D solvers for peridynamic equations, employing novel finite-volume discretizations that permit the simulation of two-way coupled fluid-structure interactions featuring nonlocal mechanics. Using recent developments in mathematical analysis, such as weakly-singular kernels for defining nonlocal generalization of the Laplacian, nonlocal 1D models will be derived to understand the fundamentals of flow-driven delamination of nanosheets where classical continuum mechanics approaches fail. Ideas from the finite-volume implementation of meshless (particle) methods will be used to design and build 3D computational tools upon standardized, open-source frameworks that can be made freely available to researchers and practitioners. The resulting computational tools will be capable of bridging scales (from the mesoscale to the continuum scale via nonlocal theories) to enable predictive simulation of flow coupled to nonlocal mechanics relevant to applications such as soft adhesion, additive manufacturing and biophysics.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.