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

基本信息

  • 批准号:
    1916876
  • 负责人:
  • 金额:
    $ 20.66万
  • 依托单位:
  • 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

项目摘要

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.
准确有效地预测材料在极端条件下的机械行为对于设计解决安全、能源和健康方面重大挑战的新型材料变得越来越重要。示例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。最近,连接弹簧的晶格被广泛用于模拟现代材料在循环载荷下的塑性变形。然而,目前可用的理论只能控制晶格弹簧模型的弹性(即可逆)变形。该奖项支持数学理论的发展,该理论能够预测和影响允许弹性和塑性变形(称为弹塑性)的晶格弹簧模型的渐近行为。新的数学框架将提供革命性的工具来加速塑性变形集中区域(已知会导致裂纹初始化)的计算,并使设计具有优异使用寿命的材料在计算上变得可行。设计的材料(例如超抗疲劳合金)最终可以制造出来,影响航空航天、汽车、微电子和生物医学等行业。因此,这项研究成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代表性不足群体对研究的参与,并对数学和工程教育产生积极影响。具有移动多面体约束的微分方程(通常称为扫描过程)将用于模拟循环载荷下弹塑性弹簧的晶格。通过开发扫掠过程的稳定性和分岔理论,该项目将识别晶格弹簧模型的机械参数,以确保对给定循环载荷。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该工具应用于此类异质材料的设计来证明,其中塑性变形的分布(响应循环载荷)尽可能保持均匀。在该设计中,将利用体积补偿晶格粒子方法将材料微观结构的数字表示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 的法定使命,并通过使用基金会的智力价值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

期刊论文数量(8)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Stabilization of the response of cyclically loaded lattice spring models with plasticity
Structurally stable families of periodic solutions in sweeping processes of networks of elastoplastic springs
弹塑性弹簧网络扫掠过程中结构稳定的周期解族
  • DOI:
    10.1016/j.physd.2020.132443
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Gudoshnikov, Ivan;Makarenkov, Oleg
  • 通讯作者:
    Makarenkov, Oleg
One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model
多边形扫掠过程的一周期稳定性分析及其弹塑性模型的应用
  • DOI:
    10.1051/mmnp/2019030
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    2.2
  • 作者:
    Gudoshnikov, Ivan;Kamenskii, Mikhail;Makarenkov, Oleg;Voskovskaia, Natalia;Rachinskiy, Dmitry
  • 通讯作者:
    Rachinskiy, Dmitry
A Continuation Principle for Periodic BV-Continuous State-Dependent Sweeping Processes
周期性BV连续状态相关扫描过程的连续原理
  • DOI:
    10.1137/19m1248613
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    2
  • 作者:
    Kamenskii, Mikhail;Makarenkov, Oleg;Wadippuli, Lakmi N.
  • 通讯作者:
    Wadippuli, Lakmi N.
Global asymptotic stability of nonconvex sweeping processes
非凸扫掠过程的全局渐近稳定性
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Oleg Makarenkov其他文献

Formation of a nontrivial finite-time stable attractor in a class of polyhedral sweeping processes with periodic input
一类具有周期输入的多面体扫描过程中非平凡有限时间稳定吸引子的形成

Oleg Makarenkov的其他文献

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{{ truncateString('Oleg Makarenkov', 18)}}的其他基金

Special Topics in Dynamical Systems: A New Mathematical Framework for the Design of Switching and Continuous Control Strategies
动力系统专题:切换和连续控制策略设计的新数学框架
  • 批准号:
    1436856
  • 财政年份:
    2014
  • 资助金额:
    $ 20.66万
  • 项目类别:
    Standard Grant

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相似海外基金

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
  • 财政年份:
    2019
  • 资助金额:
    $ 20.66万
  • 项目类别:
    Standard Grant
ULTRA-WIDEBAND 170 AND 240 GHZ CW SOURCE SWEEPING SYSTEMS
超宽带 170 和 240 GHZ CW 源扫描系统
  • 批准号:
    8363967
  • 财政年份:
    2011
  • 资助金额:
    $ 20.66万
  • 项目类别:
ULTRA-WIDEBAND 170 AND 240 GHZ CW SOURCE SWEEPING SYSTEMS
超宽带 170 和 240 GHZ CW 源扫描系统
  • 批准号:
    8172102
  • 财政年份:
    2010
  • 资助金额:
    $ 20.66万
  • 项目类别:
ULTRA-WIDEBAND 170 AND 240 GHZ CW SOURCE SWEEPING SYSTEMS
超宽带 170 和 240 GHZ CW 源扫描系统
  • 批准号:
    7956619
  • 财政年份:
    2009
  • 资助金额:
    $ 20.66万
  • 项目类别:
ULTRA-WIDEBAND 170 AND 240 GHZ CW SOURCE SWEEPING SYSTEMS
超宽带 170 和 240 GHZ CW 源扫描系统
  • 批准号:
    7723924
  • 财政年份:
    2008
  • 资助金额:
    $ 20.66万
  • 项目类别:
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