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.
翻译:由于在制订数学表达方式和决定路径行为的内部状态变量(ISVs)方面存在困难,因此,通过人文模型确定复杂材料取决于路径的行为特征和模型仍然具有挑战性。数据驱动机学习模型,如深神经网络和经常性神经网络,已成为可行的替代方法。然而,纯粹黑箱数据驱动模型,在不考虑基本物理基础的情况下,对产出输入进行绘图,却不考虑基本物理的不稳定和不准确的概括性表现。本研究报告提议在可测量材料状态的基础上,对路径依赖材料采用机械学习的物理知情数据驱动的构成模型方法。拟议的数据驱动构件模型是在考虑普遍热动力学原则的情况下设计的,在这些模型中,物质路径依赖所必需的ISVs被从材料的隐藏状态中自动推导出。描述数据驱动机获取的ISNV的演变过程,而不考虑基本的物理学基础性能和不准确性能。为了提高RNN模型模型的坚固性和精确性,在模型中引入了模型的历史步骤数量的影响,在模型中,使用土壤周期性分析方法评估了模型的稳定性。在模型下对土壤压力的演化方法进行了评估。