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

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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.