The mathematical description of elastoplasticity is a highly complex problem due to the possible change from elastic to elasto-plastic behavior (and vice-versa) as a function of the loading path. Advanced physics-based plasticity models usually feature numerous internal variables (often of tensorial nature) along with a set of evolution equations and complementary conditions. In the present work, an attempt is made to come up with a machine-learning based model that can replicate the predictions anisotropic Yld2000-2d model with homogeneous anisotropic hardening (HAH). For this, a series of modeling problems of increasing complexity is formulated and sequentially addressed using neural network models. It is demonstrated that basic fully-connected neural network models can capture the characteristic non-linearities in the uniaxial stress-strain response such as the Bauschinger effect, permanent softening or latent hardening. A neural network with gated recurrent units (GRUs) and fully-connected layer is proposed for the modeling of plane stress plasticity for arbitrary loading paths. After training and testing the model through comparison with the Yld2000-2d/HAH model, the recurrent neural network model is also used to model the multi-axial stress-strain response of a two-dimensional foam. Here, the comparison with the results from unit cell simulations provided another validation of the proposed data-driven modeling approach.

弹塑性的数学描述是一个非常复杂的问题，这是由于弹性和弹塑性行为可能随载荷路径的变化而发生变化（反之亦然）。基于物理学的高级可塑性模型通常具有许多内部变量（通常是张量性质）以及一组演化方程和互补条件。在当前的工作中，试图提出一种基于机器学习的模型，该模型可以复制具有均质各向异性硬化（HAH）的各向异性各向异性Yld2000-2d模型。为此，提出了一系列复杂性不断增加的建模问题，并使用神经网络模型依次解决了这些问题。结果表明，基本的全连接神经网络模型可以捕获单轴应力-应变响应中的特征非线性，例如包辛格效应，永久性软化或潜在性硬化。提出了一种具有门控递归单元（GRU）和全连接层的神经网络，用于对任意加载路径的平面应力可塑性进行建模。通过与Yld2000-2d / HAH模型进行比较来训练和测试模型后，还使用递归神经网络模型对二维泡沫的多轴应力-应变响应进行建模。在这里，与晶胞模拟结果的比较提供了对所提出的数据驱动建模方法的另一种验证。提出了一种具有门控递归单元（GRU）和全连接层的神经网络，用于对任意加载路径的平面应力可塑性进行建模。在通过与Yld2000-2d / HAH模型进行比较来训练和测试该模型后，还使用递归神经网络模型对二维泡沫的多轴应力-应变响应进行建模。在这里，与晶胞模拟结果的比较提供了对所提出的数据驱动建模方法的另一种验证。提出了一种具有门控递归单元（GRU）和全连接层的神经网络，用于对任意加载路径的平面应力可塑性进行建模。在通过与Yld2000-2d / HAH模型进行比较来训练和测试该模型后，还使用递归神经网络模型对二维泡沫的多轴应力-应变响应进行建模。在这里，与晶胞模拟结果的比较提供了对所提出的数据驱动建模方法的另一种验证。