A hierarchical physics-informed framework for contour prediction and toolpath spacing optimization in 3D printed continuous fiber reinforced cement-based composites

Establishing a mapping between process parameters and structural characteristics in 3D-printed continuous fiber-reinforced cementitious composites (CFRCCs) is challenging due to complex rheological behaviors and the mutual interaction between the matrix and the embedded fibers. To address this, this paper proposes a hierarchical physics-informed deep learning framework (HPC-Net) to predict the cross-sectional matrix contour and internal fiber distribution of single printed laces from process parameters. The framework utilizes a decoupled two-module architecture. Module I separates dimensional size and morphological shape predictions, incorporating volume conservation and monotonicity constraints to improve training stability and physical consistency across sparse parameter spaces. Module II employs a centroid-normalization mechanism to learn the relative fiber-matrix spatial mapping, establishing translation equivariance and preventing overfitting to absolute spatial coordinates. Validated on an orthogonal experimental dataset, HPC-Net demonstrates superior geometric fidelity and generalization capabilities compared to purely data-driven baseline models. Furthermore, the predicted 2D geometries are applied to an area-matching toolpath spacing optimization strategy for void-reduced deposition and the generation of 3D geometrical digital twins. This work establishes a geometric foundation for the computer-aided manufacturing and finite element analysis of CFRCCs structures.