SBIR Phase I: A fractional-order computational platform for the multiscale and multiphysics analysis of failure-critical systems

SBIR 第一阶段：用于故障关键系统的多尺度和多物理场分析的分数阶计算平台

• 批准号: 2212932
• 负责人: Sansit Patnaik
• 金额: $ 25.59万
• 依托单位: M3SIM, LLC
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-15 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2212932&HistoricalAwards=false
• 关键词: SBIR; Phase; fractional; order; computational

This Small Business Innovation Research (SBIR) Phase I project will develop the foundation of a fractional-calculus-based computational platform for the simulation of multiscale and multiphysics systems. This Phase I effort will focus on developing modeling capabilities for nonlinear thermomechanical fatigue and damage behavior of ductile materials and will provide important insights on both feasibility and performance of the fractional calculus approach for a class of nonlinear problems that is not only of extreme importance for scientific and industrial applications but it is also a prototypical example of multiscale and multiphysics systems.By leveraging an advanced and generalized class of operators, namely the distributed and variable-order fractional operators, this project will develop fatigue and damage mechanics simulation software capable of continuum scale computational efficiency and microscale accuracy. The resulting formulation will offer an unprecedented combination of computational efficiency, a high degree of fidelity and accuracy, and a revolutionary adaptive mathematical structure that evolves in real-time based on the underlying physics controlling the deterioration and damage process.The overarching innovation at the basis of the M3SIM software products is a one-of-its-kind computational platform based on cutting-edge distributed-variable order (DVO) fractional calculus (FC). The unique nature of DVO operators allows the new platform to perform multiscale and multiphysics analyses of complex systems at a level of accuracy and efficiency that is unattainable with traditional methods. This new approach will have profound practical implications for predictive science because it will enable a novel concept of an adaptive computational platform whose structure evolves with the underlying physics without a priori and ad hoc decisions from the user.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.

这项小型企业创新研究（SBIR）I阶段项目将为基于分数的计算平台建立基础，用于模拟多尺度和多物理系统。这阶段I的努力将着重于开发用于非线性热机械疲劳和延性材料的损害行为的建模能力，并将为一类非线性问题的分数微积分方法提供重要的见解，这对科学和工业应用不仅是非常重要的，而且它也是对多阶段的多阶型系统的极端典范，而且是多个型号的典型范围的范围。分布式和可变级分数运算符，该项目将开发能够连续规模计算效率和显微镜精度的疲劳和损坏力学模拟软件。由此产生的配方将提供计算效率，高度的忠诚度和准确性以及革命性的自适应数学结构的前所未有的组合，该结构是基于控制劣势和损害过程的基础物理学实时演变的。基于M3SIM软件的总体阶段 - 基于单位的分布 - 基于实用的分布（基于实用的），这是一种实用的分布（启用），以实用的分布（基于实用的计算）计算机 - 固定的计算机 - 固定的计算计算（键）计算（键）计算机 - 分数演算（FC）。 DVO操作员的独特性质使新平台可以以传统方法无法实现的准确性和效率进行复杂系统的多尺度和多物理分析。这种新方法将对预测科学产生深远的实践影响，因为它将使一个自适应计算平台的新颖概念在没有用户的先验和临时决定的情况下随着基础物理学的发展而发展。该奖项反映了NSF的法定任务，并通过基金会的知识优点和广泛的范围来评估。