A multiscale physics-informed neural network with RVE homogenization using isogeometric analysis for hygrothermal-electro-mechanical coupled analysis of piezoelectric composites

Physics-informed neural networks have shown potential for coupled field analysis, but their application to heterogeneous piezoelectric composites under combined thermal and moisture effects remains limited because the effective properties depend on the microstructure and the residuals of the coupled governing equations may differ substantially in scale. This paper develops a multiscale method for hygrothermal-electro-mechanical coupled analysis of piezoelectric composites. At the microscale, a representative volume element of a 1–3 piezoelectric composite is constructed, in which the cylindrical fibers are exactly represented by NURBS basis functions. The effective properties of the composite are then computed by isogeometric analysis. At the macroscale, the homogenized properties are incorporated into a parametric physics-informed neural network to predict structural responses under multiple loading and environmental conditions. The network takes the coordinates, load amplitude, temperature increment and moisture concentration increment as inputs. A nondimensional formulation is introduced to reduce training instability caused by the scale disparity among the governing equation residuals. Numerical examples show that the proposed method obtains accurate effective properties with relatively few control points. The predicted hygrothermal-electro-mechanical coupled responses agree well with the reference solutions. The proposed method provides an effective tool for multiscale modeling and response analysis of piezoelectric composites in hygrothermal environments.