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

这个小型企业创新研究(SBIR)第一阶段项目将开发一个基于分数微积分的计算平台，用于模拟多尺度和多物理系统。这一阶段的工作将集中于发展对延性材料的非线性热机械疲劳和损伤行为的建模能力，并将为分数阶微积分方法在一类非线性问题上的可行性和性能提供重要的见解，这类非线性问题不仅对科学和工业应用非常重要，而且是多尺度和多物理系统的典型例子。通过利用一类先进的和广义的算子，即分布式和变阶分数算子，该项目将开发能够连续尺度计算效率和微观尺度精度的疲劳和损伤力学仿真软件。由此产生的公式将提供前所未有的计算效率、高度保真度和准确性以及革命性的自适应数学结构，该结构基于控制劣化和破坏过程的底层物理而实时演变。M3SIM软件产品的最大创新是基于尖端分布式变阶(DVO)分数演算(FC)的同类计算平台之一。DVO操作员的独特性质使新平台能够以传统方法无法达到的精度和效率水平对复杂系统进行多尺度和多物理分析。这一新方法将对预测科学产生深远的实际影响，因为它将实现自适应计算平台的新概念，其结构与基础物理一起发展，而无需用户的先验和临时决定。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 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.