Accurate prediction of process-induced deformations in composites using layer-wise models and theory-guided probabilistic machine learning

Carbon fiber-reinforced polymer (CFRP) composites are integral to high-performance aerospace applications, offering many exceptional properties such as high specific strength and stiffness. However, despite widespread use, several challenges persist during manufacturing, one of the most prevalent being the mitigation of residual stresses and process-induced deformations (PIDs). Shortcomings of traditional process simulation-based methods commonly employed to predict PIDs often contribute to these challenges. As a result, manufacturers often grapple with inaccurate PID predictions, component mismatches during assembly, increased production times, and compromised mechanical performance. This paper proposes an alternative method for accurately predicting PIDs in composite parts. First, a finite element (FE) solution scheme based on onedimensional (1D) models and the Carrera Unified Formulation (CUF), is employed to predict PIDs for L-shaped laminates in a defined design space. Then, the virtual simulation data is mapped to a reduced-order theory-guided domain and modeled using Gaussian Process Regression (GPR), a probabilistic machine learning technique. The GPR model is then iteratively retrained to calibrate simulation predictions by incorporating limited real-world experimental data and creating an adaptive probabilistic model with a data-driven uncertainty structure. The effectiveness of the proposed method is demonstrated by accurately predicting the cured deformed shape of an L-shaped cross-ply laminate using just five experiments. The method provides a cost-efficient framework for predicting, understanding, and potentially mitigating PIDs in composite parts.