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: 1916876
• 负责人: Oleg Makarenkov
• 金额: $ 20.66万
• 依托单位: University of Texas at Dallas
• 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 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1916876&HistoricalAwards=false
• 关键词: Collaborative; Research; Sweeping; Process; Framework; 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.

在极端条件下对材料机械行为的准确预测对于应对安全，能源和健康方面的巨大挑战的新型材料的设计变得越来越重要。这些示例范围从微芯片中的微米大小的焊缝到飞机的关键结构部分。材料在循环载荷下形成的局部塑料（即不可逆的）变形代表了损失性能和材料失败的最典型途径。最近，连接弹簧的格子被广泛用于模拟循环载荷下现代材料的塑性变形。但是，在当前可用的理论中只能控制晶格弹簧模型的弹性（即可逆的）变形。该奖项支持了数学理论的发展，其能力可以预测和影响晶格弹簧模型的渐近行为，这些模型允许弹性和塑料变形（称为弹性层状）。新的数学框架将提供一种革命性的工具，以加速塑料变形浓缩物（已知会导致裂纹初始化）的区域的计算，并使其在计算上对于使用卓越服务寿命的设计材料在计算上可行。设计的材料（例如，耐超疲劳合金）最终可以生产以影响航空航天，汽车，微电子和生物医学等行业。因此，这项研究的结果将使美国社会和国家安全受益。多学科的合作将有助于扩大代表性不足的小组参与研究的参与，并积极影响数学和工程教育。具有移动的多面体约束（通常称为扫描过程）的不同方程将用于模拟cyclic载荷下弹性弹簧的晶格。通过开发稳定过程的稳定性和分叉理论，该项目将确定晶格弹簧模型的机械参数，以确保对给定给定的环状负载确保独特的周期性响应（有限的定期稳定或渐近稳定或渐近响应（是否隔离））。发现的动力学行为将用于有效计算塑性变形的渐近分布。该工具的性能将通过将其应用于此类异质材料的设计，以使塑性变形的分布（对环状负荷的响应）保持尽可能均匀。在此设计中，将使用体积补偿的晶状体方法将材料微结构的数字表示形式映射到晶格弹簧模型。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的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评论标准来评估值得支持的。