We propose a physics informed, neural network-based elasto-viscoplasticity (NN-EVP) constitutive modeling framework for predicting the flow response in metals as a function of underlying grain size. The developed NN-EVP algorithm is based on input convex neural networks as a means to strictly enforce thermodynamic consistency, while allowing high expressivity towards model discovery from limited data. It utilizes state-of-the-art machine learning tools within PyTorch's high-performance library providing a flexible tool for data-driven, automated constitutive modeling. To test the performance of the framework, we generate synthetic stress-strain curves using a power law-based model with phenomenological hardening at small strains and test the trained model for strain amplitudes beyond the training data. Next, experimentally measured flow responses obtained from uniaxial deformations are used to train the framework under large plastic deformations. Ultimately, the Hall-Petch relationship corresponding to grain size strengthening is discovered by training flow response as a function of grain size, also leading to efficient extrapolation. The present work demonstrates a successful integration of neural networks into elasto-viscoplastic constitutive laws, providing a robust automated framework for constitutive model discovery that can efficiently generalize, while also providing insights into predictions of flow response and grain size-property relationships in metals and metallic alloys under large plastic deformations.

翻译：我们提出了一种基于物理信息的神经网络弹-粘塑性（NN-EVP）本构建模框架，用于预测金属流动响应与底层晶粒尺寸的函数关系。所开发的NN-EVP算法基于输入凸神经网络，以此严格保证热力学一致性，同时允许从有限数据中实现高表达性的模型发现。该算法利用PyTorch高性能库中先进的机器学习工具，为数据驱动的自动化本构建模提供灵活工具。为测试框架性能，我们使用基于幂律模型并包含小应变下现象学硬化的方法生成合成应力-应变曲线，并测试训练模型在超出训练数据范围的应变幅值下的表现。随后，利用单轴变形实验测得的流动响应，在大塑性变形条件下训练该框架。最终，通过训练流动响应与晶粒尺寸的函数关系，发现了对应于晶粒强化的Hall-Petch关系，并实现了高效的外推。本研究成功展示了神经网络与弹-粘塑性本构律的整合，提供了一个鲁棒的自动化本构模型发现框架，该框架不仅能高效泛化，还能在大塑性变形条件下为金属及金属合金的流动响应及晶粒尺寸-性能关系预测提供见解。