Physics-Informed Deep Learning Constitutive Model for Anisotropic and Pressure-Dependent Behavior of Short Fiber-Reinforced Polymers

Short fiber-reinforced polymers (SFRPs) exhibit complex anisotropic, nonlinear, and pressure-dependent behavior due to their heterogeneous microstructures. Conventional constitutive models, while accurate, require extensive parameter calibration and may lack generalization capability under varied loading conditions. In this study, a physics-informed deep learning (PIDL) constitutive framework is proposed that integrates the governing physical laws with the flexibility of neural networks. The model employs long short-term memory (LSTM) networks to capture path-dependent behaviors and utilizes scalar invariants consistent with transverse isotropy to ensure thermodynamic consistency, objectivity, and material symmetry. The neural network is trained using synthetic data generated from a validated continuum-mechanical model for SFRPs, including elasto-plastic behavior and anisotropy. To validate the PIDL model, an open-hole tensile (OHT) test is simulated, and the predicted stresses are compared against those obtained from the classical constitutive model. While the initial PIDL model showed limitations under complex multiaxial stress states, a retraining strategy using randomly generated loading paths significantly improved its predictive accuracy. This study demonstrates the potential of physics-informed machine learning for developing generalizable and efficient data-driven constitutive models for complex composite materials.