Recurrent neural networks (RNNs) learn the constitutive law of viscoelasticity

Abstract

Recurrent neural networks (RNNs) have demonstrated very impressive performances in learning sequential data, such as in language translation and music generation. Here, we show that the intrinsic computational aspect of RNNs is very similar to that of classical stress update algorithms in modeling history-dependent materials with an emphasis on viscoelasticity. Several numerical examples are designed, including 1-dimensional and 3-dimensional cases, which testify the ability of RNN model to compute the viscoelastic response when predicting on unseen test data. Additionally, it is found that the RNN model trained only on linear and step strain inputs can perform very well on prediction of completely different quadratic strain inputs, demonstrating certain level of generalization ability in extrapolation. Moreover, it is observed that the extrapolation ability depends on the types of strain inputs. The performance is better for continuous strain inputs than that for jump strain inputs. The differences in the generalization ability of RNN models in viscoelasticity and other history-dependent materials are discussed. It suggests that RNN data-driven modeling can be an alternative to the conventional viscoelasticity models.