Data-driven constitutive modeling frameworks based on neural networks and
classical representation theorems have recently gained considerable attention
due to their ability to easily incorporate constitutive constraints and their
excellent generalization performance. In these models, the stress prediction
follows from a linear combination of invariant-dependent coefficient functions
and known tensor basis generators. However, thus far the formulations have been
limited to stress representations based on the classical Rivlin and Ericksen
form, while the performance of alternative representations has yet to be
investigated. In this work, we survey a variety of tensor basis neural network
models for modeling hyperelastic materials in a finite deformation context,
including a number of so far unexplored formulations which use theoretically
equivalent invariants and generators to Finger-Rivlin-Ericksen. Furthermore, we
compare potential-based and coefficient-based approaches, as well as different
calibration techniques. Nine variants are tested against both noisy and
noiseless datasets for three different materials. Theoretical and practical
insights into the performance of each formulation are given.

基于数据驱动的神经网络和经典表示定理的本构建模框架因其易于整合本构约束和卓越的泛化性能而受到广泛关注。本研究通过测试多种不同张量基生成器的模型，对有限变形情况下的高弹性材料进行建模，包括一些尚未探索使用与 Finger-Rivlin-Ericksen 理论等效的不变量和生成器的公式。此外，我们比较了基于势函数和系数的方法以及不同的校准技术，并对三种不同材料的噪声和无噪声数据集进行了九个变体的测试，提供了每种公式性能的理论和实用洞察。