A recurrent neural network (RNN) based model is developed as a surrogate to predict nonlinear plastic response under multiaxial loading. The RNN-based model is trained and tested on stress versus strain curves generated using a numerical solution based on the classical radial return method. Besides simply learning the basic constitutive relationship, a novel approach is taken to enforce certain physical conditions. Specifically, regularization is employed to maintain non-negative plastic power density throughout the loading history thereby ensuring monotonically increasing plastic work and thermodynamic consistency. Enforcing physics in this manner permits coupling of the data-driven RNN approach with physics-based knowledge and laws. This has the effect of reducing the necessary amount of data and ensuring known physical laws are not violated. Since, once trained, the model need not perform the expensive task of solving nonlinear equations, its efficiency is orders of magnitude greater than its numerical counterpart. The RNN-based model has been trained on varied sets of data and the accuracy on test datasets validated. The developed model is general and robust and has widespread application such as in the simulation of metal forming, large scale plasticity, and part life prediction.

开发了一种基于循环神经网络 (RNN) 的模型，作为预测多轴载荷下非线性塑性响应的替代方法。基于 RNN 的模型在使用基于经典径向返回方法的数值解生成的应力与应变曲线上进行训练和测试。除了简单地学习基本的本构关系外，还采用了一种新颖的方法来强制执行某些物理条件。具体而言，正则化用于在整个加载历史中保持非负塑性功率密度，从而确保单调增加塑性功和热力学一致性。以这种方式加强物理学允许将数据驱动的 RNN 方法与基于物理学的知识和定律结合起来。这具有减少必要数据量并确保不违反已知物理定律的效果。由于一旦经过训练，该模型不需要执行求解非线性方程的昂贵任务，因此其效率比其数值对应物高几个数量级。基于 RNN 的模型已经在不同的数据集上进行了训练，并且验证了测试数据集的准确性。所开发的模型具有通用性和鲁棒性，在金属成形模拟、大规模塑性和零件寿命预测等方面具有广泛的应用。