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.

我们提出了一个泛化的深度神经网络方法，用于以分位回归捕捉不确定性来建模应力作为状态函数。我们通过应用随机微分方程将这些模型扩展到单轴冲击力学，展示了一个使用案例，并提供了一个实施这种不确定性感知应力函数的框架。我们对公开可用和新呈现的数据集进行了实验证明我们的方法优于领先的本构、机器学习和迁移学习方法在应力和冲击力学建模方面。我们还提供了一个框架，以优化材料参数，根据多个竞争的冲击场景。

深度神经网络在不确定应力函数中的应用及对冲击力学的拓展