Stress representations for tensor basis neural networks: alternative
  formulations to Finger-Rivlin-Ericksen
Jan N. Fuhg Nikolaos Bouklas Reese E. Jones
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.