Collaborative Research: A Sweeping Process Framework to Control the Dynamics of Elastoplastic Systems

协作研究：控制弹塑性系统动力学的全面过程框架

• 批准号: 1916878
• 负责人: Yang Jiao
• 金额: $ 13.41万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1916878&HistoricalAwards=false
• 关键词: Collaborative; Research; Sweeping; Process; Framework

Accurate and efficient prediction of the mechanical behavior of materials under extreme conditions is becoming increasingly crucial for the design of novel materials that address the grand challenges in security, energy and health. The examples range from micron-sized solder joints in micro-chips to crucial structural parts of airplanes. Localized plastic (i.e. irreversible) deformations that the material develops under cyclic loading represent the most typical route to the loss of performance and material's failure. Recently, lattices of connected springs became widely used to model plastic deformations of modern materials under cyclic loading. However, only elastic (i.e. reversible) deformations of lattice spring models can be controlled within the currently available theory. This award supports the development of a mathematical theory with the capability to predict and influence the asymptotic behavior of lattice spring models that are allowed to deform both elastically and plastically (termed elastoplastically). The new mathematical framework will provide a revolutionary tool to accelerate computation of the regions where the plastic deformations concentrate (known to cause crack initialization) and will make it computationally feasible to design materials with superior service lifetime. The designed materials (e.g., super fatigue resistant alloys) can be eventually manufactured to impact such industries as aerospace, automobile, microelectronics and biomedical. Therefore, the results from this research will benefit the U.S. society and national security. The multi-disciplinary collaboration will help broaden participation of underrepresented groups in research and positively impact mathematical and engineering education.Differential equations with moving polyhedral constraints (commonly known as sweeping processes) will be used to model the lattices of elastoplastic springs under cyclic loading. By developing a theory of stability and bifurcations for sweeping processes, this project will identify the mechanical parameters of lattice spring models that ensure a unique periodic response (finite-time stable or asymptotic) or co-existing periodic responses (isolated or not) to a cyclic loading given. The dynamical behavior found will be used to efficiently compute the asymptotic distribution of plastic deformations. The performance of this tool will be demonstrated by applying it to the design of such heterogeneous materials for which the distribution of plastic deformations (in the response to cyclic loading) stays as uniform as possible. In this design, the Volume-Compensated Lattice-Particle method will be utilized to map the digital representation of the material microstructure to a lattice spring model. The design will be experimentally validated using 3D-printed sample composite materials.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.

准确和有效地预测材料在极端条件下的力学行为对于设计解决安全、能源和健康方面的重大挑战的新型材料正变得越来越重要。这些例子的范围从微芯片中的微米级焊点到飞机的关键结构部件。材料在循环载荷作用下产生的局部塑性(即不可逆)变形是导致性能损失和材料失效的最典型途径。近年来，连通弹簧格子被广泛用于模拟现代材料在循环载荷作用下的塑性变形。然而，只有格子弹簧模型的弹性(即可逆)变形才能控制在现有的理论范围内。该奖项支持一种数学理论的发展，该理论能够预测和影响允许弹性和塑性(称为弹塑性)变形的格子弹簧模型的渐近行为。新的数学框架将提供一个革命性的工具来加速计算塑性变形集中的区域(已知会导致裂纹初始化)，并将使设计具有更高使用寿命的材料在计算上可行。设计的材料(例如，超级耐疲劳合金)最终可以制造出来，对航空航天、汽车、微电子和生物医学等行业产生影响。因此，这项研究的结果将有利于美国社会和国家安全。多学科合作将有助于扩大未被充分代表的群体在研究中的参与，并对数学和工程教育产生积极影响。带有移动多面体约束的微分方程式(通常称为扫掠过程)将用于模拟循环载荷下弹塑性弹簧的晶格。通过发展扫描过程的稳定性和分叉理论，本项目将确定格子弹簧模型的力学参数，以确保对给定的循环载荷具有唯一的周期响应(有限时间稳定或渐近)或共存的周期响应(孤立或非孤立)。所发现的动力学行为将被用于有效地计算塑性变形的渐近分布。这种工具的性能将通过将其应用于这种非均质材料的设计来演示，对于这些非均质材料，塑性变形(对循环加载的响应)的分布尽可能保持均匀。在本设计中，将利用体积补偿格子粒子方法将材料微观结构的数字表示映射到格子弹簧模型。该设计将使用3D打印样品复合材料进行实验验证。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。

项目成果

Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling

模拟细胞外基质微机械耦合调节的细胞迁移

• DOI: 10.1103/physreve.100.043303
• 发表时间: 2019
• 期刊: PHYSICAL REVIEW E
• 影响因子: 2.4
• 作者: Zheng Yu;Nan Hanging;Liu Yanping;Fan Qihui;Wang Xiaochen;Liu Ruchuan;Liu Liyu;Ye Fangfu;Sun Bo;Jiao Yang
• 通讯作者: Jiao Yang