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

这个基于计算和数据的科学与工程(CDS&Amp；E)项目将通过实现与生物医学(如何在手术后将组织层粘合在一起)以及涂层和密封剂的开发(如何确保干燥的油漆保持附着在表面上)相关的复杂机械问题的预测性模拟，为促进国家繁荣和经济福祉做出贡献。大多数人都经历过从表面剥离一块胶带或试图举起粘在湿玻璃桌面上的薄物体的常见挑战。从油漆和自制家居修理到尿布和卫生用品，软涂层涉及弹性材料与刚性基材的流体层中介粘合。在真实世界的场景中，准确模拟粘结和脱粘过程(包括材料破坏)的能力仍然是一个挑战。这笔拨款支持的基础研究将通过开发理论来推动科学进步，这些理论将导致快速而准确的模拟工具，能够处理薄层流体和柔软、弹性表面之间的复杂相互作用，这些表面可以因流体的流动而附着、分离甚至撕裂。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工作人员的多样性。这笔赠款将通过构建可处理的将非局部机械响应与流体流动耦合的1D模型，实现对流动诱导的机械变形的预测性、多尺度模拟，从而创建用于动力学方程的3D解算器，采用新颖的有限体积离散化，允许模拟具有非局部力学特征的双向耦合流固相互作用。利用数学分析中的最新发展，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1D模型，以理解在经典连续介质力学方法失效的情况下纳米薄片流动驱动分层的基本原理。无网格(粒子)方法的有限体积实现的想法将被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连接尺度(通过非局部理论从介观尺度到连续尺度)，以实现与与软粘着、添加剂制造和生物物理学等应用相关的非局部力学耦合的流动的预测性模拟。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。

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.