Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical relationships were derived through experimentation and curve fitting. Recently, to automate the constitutive modeling process, data-driven approaches based on neural networks have been explored. While initial naive approaches violated established mechanical principles, recent efforts concentrate on designing neural network architectures that incorporate physics and mechanistic assumptions into machine-learning-based constitutive models. For history-dependent materials, these models have so far predominantly been restricted to small-strain formulations. In this work, we develop a finite strain plasticity formulation based on thermodynamic potentials to model mixed isotropic and kinematic hardening. We then leverage physics-augmented neural networks to automate the discovery of thermodynamically consistent constitutive models of finite strain elastoplasticity from uniaxial experiments. We apply the framework to both synthetic and experimental data, demonstrating its ability to capture complex material behavior under cyclic uniaxial loading. Furthermore, we show that the neural network enhanced model trains easier than traditional phenomenological models as it is less sensitive to varying initial seeds. Our model’s ability to generalize beyond the training set underscores its robustness and predictive power. By automating the discovery of hardening models, our approach eliminates user bias and ensures that the resulting constitutive model complies with thermodynamic principles, thus offering a more systematic and physics-enforced framework.

中文翻译：

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从单轴实验中自动发现有限应变弹塑性的模型


本构建模是力学的核心，它允许我们在给定的机械设置中将应变映射到材料的应力上。从历史上看，研究人员依赖于现象学建模，其中简单的数学关系是通过实验和曲线拟合得出的。最近，为了实现本构建模过程的自动化，人们探索了基于神经网络的数据驱动方法。虽然最初的幼稚方法违反了既定的机械原理，但最近的努力集中在设计神经网络架构，将物理和机械假设整合到基于机器学习的本构模型中。对于历史依赖性材料，到目前为止，这些模型主要局限于小应变公式。在这项工作中，我们开发了一种基于热力学势的有限应变塑性公式，用于模拟混合各向同性和运动硬化。然后，我们利用物理增强神经网络从单轴实验中自动发现有限应变弹塑性的热力学一致本构模型。我们将该框架应用于合成和实验数据，证明了它在循环单轴载荷下捕获复杂材料行为的能力。此外，我们表明，神经网络增强的模型比传统的现象学模型更容易训练，因为它对变化的初始种子不太敏感。我们的模型在训练集之外进行泛化的能力强调了它的稳健性和预测能力。通过自动发现硬化模型，我们的方法消除了用户偏差，并确保生成的本构模型符合热力学原理，从而提供了一个更加系统和物理强制的框架。