Use of Deep Neural Networks for Uncertain Stress Functions with Extensions to Impact Mechanics
This work addresses the problem of accurately predicting material stress under complex conditions for engineers and researchers, though it appears incremental by combining existing techniques in a novel application.
The authors tackled the challenge of modeling uncertain stress functions in materials by proposing a deep neural network approach with quantile regression, extending it to impact mechanics using stochastic differential equations, and demonstrated competitive performance against existing methods on public and new datasets.
Stress-strain curves, or more generally, stress functions, are an extremely important characterization of a material's mechanical properties. However, stress functions are often difficult to derive and are narrowly tailored to a specific material. Further, large deformations, high strain-rates, temperature sensitivity, and effect of material parameters compound modeling challenges. We propose a generalized deep neural network approach to model stress as a state function with quantile regression to capture uncertainty. We extend these models to uniaxial impact mechanics using stochastic differential equations to demonstrate a use case and provide a framework for implementing this uncertainty-aware stress function. We provide experiments benchmarking our approach against leading constitutive, machine learning, and transfer learning approaches to stress and impact mechanics modeling on publicly available and newly presented data sets. We also provide a framework to optimize material parameters given multiple competing impact scenarios.