Prediction evolution animation with training 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.

由于非晶态形状记忆聚合物（amorphous shape memory polymers, SMPs）的行为复杂，传统本构模型常受限于材料特异性、曲线拟合难度大、应力计算依赖历史状态，且控制方程分步求解易导致误差累积。本研究提出一种物理信息人工神经网络（physics-informed artificial neural network, PIANN），将传统神经网络与基于应变的相变框架相结合，用于预测非晶态SMPs的本构行为。该模型通过五个温度-应力数据集和四个温度-应变数据集进行验证，包括四种SMPs的实验数据及一个广泛接受的模型的模拟结果。PIANN可预测四种关键形状记忆行为：热编程过程中的应力演化、冷热编程后的应力恢复，以及加热阶段的自由应变恢复。值得注意的是，其在训练时未使用任何加热数据的情况下，仍能准确预测加热过程中的恢复应变。与实验数据对比显示，模型在编程（冷却）和恢复（加热）阶段均具有优异的一致性。更显著的是，训练集仅需两条温度-应力曲线即可实现这一性能。总体而言，PIANN通过消除历史依赖、提高曲线拟合精度及显著提升计算效率，解决了SMP建模中的常见挑战。这项工作为SMP通用模型的开发迈出了重要一步。