Abstract：Functionally graded materials (FGMs) are promising for advanced structures due to their excellent mechanical properties, but determining the spatial distribution of their material parameters remains challenging. This paper proposes a physics-informed neural network (PINN) framework to solve this inverse problem. The framework consists of two subnetworks: the strain network used to smooth the noisy strain data, and the elasticity network designed to learn physical information from equilibrium equation. The total loss function consists of data loss, PDE loss, and regularization loss, and the spatial distribution of material parameters is obtained by minimizing the total loss. To calibrate the predicted Young’s modulus, a Saint-Venant principle-based method is proposed. Compared with existing methods that require known boundary stresses, this method only requires experimentally measured loading forces. Numerical results show that the proposed framework achieves accurate identification of FGM material parameters even under high levels of noise. This study provides an effective approach for the inverse design and non-destructive evaluation of FGMs.
2026, Vol. 47 
