Characterization and modeling of path-dependent behaviors of complex materials by phenomenological models remains challenging due to difficulties in formulating mathematical expressions and internal state variables (ISVs) governing path-dependent behaviors. Data-driven machine learning models, such as deep neural networks and recurrent neural networks (RNNs), have become viable alternatives. However, pure black-box data-driven models mapping inputs to outputs without considering the underlying physics suffer from unstable and inaccurate generalization performance. This study proposes a machine-learned physics-informed data-driven constitutive modeling approach for path-dependent materials based on the measurable material states. The proposed data-driven constitutive model is designed with the consideration of universal thermodynamics principles, where the ISVs essential to the material path-dependency are inferred automatically from the hidden state of RNNs. The RNN describing the evolution of the data-driven machine-learned ISVs follows the thermodynamics second law. To enhance the robustness and accuracy of RNN models, stochasticity is introduced to model training. The effects of the number of RNN history steps, the internal state dimension, the model complexity, and the strain increment on model performances have been investigated. The effectiveness of the proposed method is evaluated by modeling soil material behaviors under cyclic shear loading using experimental stress–strain data.

由于难以制定数学表达式和控制路径依赖行为的内部状态变量 (ISV)，通过唯象模型对复杂材料的路径依赖行为进行表征和建模仍然具有挑战性。数据驱动的机器学习模型，例如深度神经网络和递归神经网络 (RNN)，已成为可行的替代方案。然而，纯粹的黑盒数据驱动模型将输入映射到输出而不考虑底层物理，其泛化性能不稳定且不准确。本研究提出了一种基于可测量材料状态的路径相关材料的机器学习物理信息数据驱动本构建模方法。所提出的数据驱动本构模型是在考虑通用热力学原理的情况下设计的，其中对物质路径依赖至关重要的 ISV 是从 RNN 的隐藏状态自动推断出来的。描述数据驱动的机器学习 ISV 演变的 RNN 遵循热力学第二定律。为了提高 RNN 模型的鲁棒性和准确性，将随机性引入模型训练。研究了 RNN 历史步数、内部状态维度、模型复杂度和应变增量对模型性能的影响。通过使用实验应力-应变数据模拟循环剪切载荷下的土壤材料行为来评估所提出方法的有效性。描述数据驱动的机器学习 ISV 演变的 RNN 遵循热力学第二定律。为了提高 RNN 模型的鲁棒性和准确性，将随机性引入模型训练。研究了 RNN 历史步数、内部状态维度、模型复杂度和应变增量对模型性能的影响。通过使用实验应力-应变数据模拟循环剪切载荷下的土壤材料行为来评估所提出方法的有效性。描述数据驱动的机器学习 ISV 演变的 RNN 遵循热力学第二定律。为了提高 RNN 模型的鲁棒性和准确性，将随机性引入模型训练。研究了 RNN 历史步数、内部状态维度、模型复杂度和应变增量对模型性能的影响。通过使用实验应力-应变数据模拟循环剪切载荷下的土壤材料行为来评估所提出方法的有效性。