Supplementary materials from Toward a general physics-informed neural network for amorphous shape memory polymer modelling

Due to the complex behaviour of amorphous shape memory polymers (SMPs), traditional constitutive models often struggle with material-specific limitations, challenging curve-fitting, history-dependent stress calculations and error accumulation from stepwise calculation for governing equations. In this study, we propose a physics-informed artificial neural network (PIANN) that integrates a conventional neural network with a strain-based phase transition framework to predict the constitutive behaviour of amorphous SMPs. The model is validated using five temperature–stress datasets and four temperature–strain datasets, including experimental data from four types of SMPs and simulation results from a widely accepted model. PIANN predicts four key shape memory behaviours: stress evolution during hot programming, stress recovery following both cold and hot programming and free strain recovery during heating branch. Notably, it predicts recovery strain during heating without using any heating data for training. Comparisons with experimental data show excellent agreement in both programming (cooling) and recovery (heating) branches. Remarkably, the model achieves this performance with as few as two temperature–stress curves in the training set. Overall, PIANN addresses common challenges in SMP modelling by eliminating history dependence, improving curve-fitting accuracy and significantly enhancing computational efficiency. This work represents a substantial step forward in developing generalizable models for SMPs.