Machine learning techniques are increasingly used to predict material behavior in scientific applications and offer a significant advantage over conventional numerical methods. In this work, an Artificial Neural Network (ANN) model is used in a finite element formulation to define the flow law of a metallic material as a function of plastic strain ${\varepsilon }^p$, plastic strain rate ${\stackrel{\mathit{.}}{\varepsilon }}^p$ and temperature $T$. First, we present the general structure of the neural network, its operation and focus on the ability of the network to deduce, without prior learning, the derivatives of the flow law with respect to the model inputs. In order to validate the robustness and accuracy of the proposed model, we compare and analyze the performance of several network architectures with respect to the analytical formulation of a Johnson–Cook behavior law for a 42CrMo4 steel. In a second part, after having selected an Artificial Neural Network architecture with 2 hidden layers, we present the implementation of this model in the Abaqus Explicit computational code in the form of a VUHARD subroutine. The predictive capability of the proposed model is then demonstrated during the numerical simulation of two test cases: the necking of a circular bar and a Taylor impact test. The results obtained show a very high capability of the ANN to replace the analytical formulation of a Johnson–Cook behavior law in a finite element code, while remaining competitive in terms of numerical simulation time compared to a classical approach.

机器学习技术越来越多地用于预测科学应用中的材料行为，并提供优于传统数值方法的显着优势。在这项工作中，人工神经网络 (ANN) 模型用于有限元公式，以将金属材料的流动规律定义为塑性应变的函数${\varepsilon }^{磷}$, 塑性应变率 ${\stackrel{\mathit{.}}{\varepsilon }}^{磷}$ 和温度 $吨$. 首先，我们介绍了神经网络的一般结构、它的操作，并重点介绍了网络在无需先验学习的情况下推断流动定律相对于模型输入的导数的能力。为了验证所提出模型的稳健性和准确性，我们比较和分析了几种网络架构的性能，这些架构涉及 42CrMo4 钢的 Johnson-Cook 行为定律的解析公式。在第二部分中，在选择了具有 2 个隐藏层的人工神经网络架构后，我们以 VUHARD 子例程的形式在 Abaqus 显式计算代码中展示了该模型的实现。然后在两个测试案例的数值模拟期间证明了所提出模型的预测能力：圆棒的颈缩和泰勒冲击测试。