Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. In this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.

中文翻译：

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热弹性多凸神经网络模型


诸如神经网络之类的机器学习函数表示已被证明是本构建模的优秀构造，因为它们能够灵活地表示高度非线性数据，并且能够合并本构约束，这也使它们能够很好地推广到不可见的数据。在这项工作中，我们通过指定以变形不变量和温度表示的亥姆霍兹自由能扩展的热力学和材料理论要求，将多凸超弹性神经网络框架扩展到（各向同性）热超弹性。提出并讨论了确保变形方面的多凸性和温度方面的凹性的不同公式。此外，物理增强神经网络还使用最近提出的稀疏化算法进行校准，该算法不仅旨在拟合训练数据，而且还惩罚活动参数的数量，从而防止低数据状态下的过度拟合并促进泛化。所提出的框架的性能在合成数据上得到了证明，这些数据说明了预期的热机械现象，以及现有的与温度相关的单轴拉伸和拉伸扭转实验数据集。