A thermodynamics-constrained neural network with mechanical encoding for nonlinear viscoelastic modelling from sparse data

Abstract Accurately predicting the nonlinear viscoelastic behaviour of materials such as polymers remains a key challenge, particularly when only limited experimental data are available. While recurrent neural networks (RNNs) are often used to capture path-dependent material responses, they suffer from training instabilities and poor extrapolation capabilities. This study addresses this gap by developing an alternative approach with a hybrid, thermodynamically-based framework that combines a linear generalised Maxwell model with a multilayer perceptron (MLP). The Maxwell model acts as a ‘physics-based’ encoding layer, providing interpretable internal variables that represent the material’s deformation history. Unlike RNNs, MLPs are better suited for capturing complex nonlinear relationships without relying on memory cells, thereby improving generalisation beyond the training domain. The parameters of the mechanical model and the neural network are jointly optimised. A residual connection allows the network to correct the Maxwell model’s output. The proposed model, referred to as Mech-TANN, accurately reproduces nonlinear viscoelastic behaviour using only forty noisy data points from synthetic shear tests. It achieves less than 7% prediction error on test data with a noise level of 2% of the maximum signal amplitude. With four times the data, the precision improves tenfold. It demonstrates excellent extrapolation to larger strain amplitudes and unseen loading types, including relaxation tests. The combination of mechanical encoding and thermodynamic constraints yields a data-efficient and generalisable modelling framework that benefits from physically motivated inductive bias for complex time-dependent materials.