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Data-driven constitutive modeling frameworks based on neural networks andclassical representation theorems have recently gained considerable attentiondue to their ability to easily incorporate constitutive constraints and theirexcellent generalization performance. In these models, the stress predictionfollows from a linear combination of invariant-dependent coefficient functionsand known tensor basis generators. However, thus far the formulations have beenlimited to stress representations based on the classical Rivlin and Ericksenform, while the performance of alternative representations has yet to beinvestigated. In this work, we survey a variety of tensor basis neural networkmodels for modeling hyperelastic materials in a finite deformation context,including a number of so far unexplored formulations which use theoreticallyequivalent invariants and generators to Finger-Rivlin-Ericksen. Furthermore, wecompare potential-based and coefficient-based approaches, as well as differentcalibration techniques. Nine variants are tested against both noisy andnoiseless datasets for three different materials. Theoretical and practicalinsights into the performance of each formulation are given.

Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksen