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<p>The mechanical behavior of Short Fiber Reinforced Composites (SFRC) is highly nonlinear and challenging to predict due to multi-scale coupling effects. Although machine learning (ML) offers promising predictive capabilities, existing studies often fall short in accurately modeling the complex elastoplastic response of SFRC. This study introduces an innovative approach combining single-task and multi-task Gaussian Process Regression (GPR) with the Bell number—a concept from combinatorics—to optimize the model structure for high-fidelity prediction of stress-strain curves. It is important to note that the datasets used to train the GPR models were obtained from a commercial software (Digimat). Through theoretical modeling and systematic validation, our optimized GPR model achieved exceptional performance with Coefficient of Determination (R²) values up to 0.99 and Mean Squared Error (MSE) as low as 10<sup>–11</sup>, effectively capturing key nonlinear characteristics. Predicted plastic strain exhibits a local correlation peak near ~ 25% fiber volume fraction in simulation; higher effective aspect ratios correlate with improved simulated stress transfer. Several cross-validation strategies are benchmarked to evaluate robustness. The study also evaluates cross-validation strategies to ensure robustness. This work provides a novel data-driven framework for composite performance prediction, demonstrating the strong potential of Bell-number-optimized GPR in modeling complex nonlinear material behavior within the scope of the employed simulation data.</p>

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Prediction of Stress-Strain Behavior of Short Fiber-Reinforced Composite Materials Based on Group-Optimized Gaussian Process Regression

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Shuiwen Zhu,
  • Wenqi Xing,
  • Wei Zhang,
  • Guilian Xue

摘要

The mechanical behavior of Short Fiber Reinforced Composites (SFRC) is highly nonlinear and challenging to predict due to multi-scale coupling effects. Although machine learning (ML) offers promising predictive capabilities, existing studies often fall short in accurately modeling the complex elastoplastic response of SFRC. This study introduces an innovative approach combining single-task and multi-task Gaussian Process Regression (GPR) with the Bell number—a concept from combinatorics—to optimize the model structure for high-fidelity prediction of stress-strain curves. It is important to note that the datasets used to train the GPR models were obtained from a commercial software (Digimat). Through theoretical modeling and systematic validation, our optimized GPR model achieved exceptional performance with Coefficient of Determination (R²) values up to 0.99 and Mean Squared Error (MSE) as low as 10–11, effectively capturing key nonlinear characteristics. Predicted plastic strain exhibits a local correlation peak near ~ 25% fiber volume fraction in simulation; higher effective aspect ratios correlate with improved simulated stress transfer. Several cross-validation strategies are benchmarked to evaluate robustness. The study also evaluates cross-validation strategies to ensure robustness. This work provides a novel data-driven framework for composite performance prediction, demonstrating the strong potential of Bell-number-optimized GPR in modeling complex nonlinear material behavior within the scope of the employed simulation data.