Physics-Informed Machine Learning for Predicting Buckling Performance and Damage Evolution in Graphene Reinforced Basalt/Epoxy Composites

Technical Summary: Physics-Informed Machine Learning for Predicting Buckling Performance and Damage Evolution in Graphene Reinforced Basalt/Epoxy Composites

Problem Statement
Basalt fiber-reinforced polymer composites (BFRCs) offer a sustainable, high-strength alternative to glass and carbon fibers for lightweight structural applications. However, their utility in advanced engineering is constrained by weak fiber–matrix interfacial adhesion, premature damage initiation, and limited compressive stability. Specifically, basalt composites often suffer from micro-buckling and fiber instability under compressive loads, leading to delamination and reduced damage tolerance. While nanomaterial functionalization, particularly with reduced graphene oxide (rGO), has shown promise in enhancing matrix stiffness and interfacial bonding, existing research typically addresses these improvements in isolation—either modifying the matrix or coating the fibers. There is a lack of integrated frameworks that simultaneously explore dual-phase functionalization and translate these nanoscale enhancements into macroscale structural stability, particularly under nonlinear buckling and progressive damage conditions. Furthermore, traditional design optimization relies on computationally expensive finite element analysis (FEA), making the exploration of vast design spaces (geometric parameters and stacking sequences) impractical.

Methodology
The study proposes an integrated experimental–computational framework combining dual-phase rGO functionalization, multiscale modeling, and physics-informed machine learning (ML).

1. Material Fabrication and Characterization:
   Four composite systems were fabricated using the Vacuum Assisted Resin Transfer Molding (VARTM) technique:

   • BEC: Basalt/epoxy (control).
   • BREC: rGO-modified epoxy matrix (0.75 wt.% rGO).
   • CBEC: rGO-coated basalt fibers (0.3 wt.% rGO via electrophoretic deposition).
   • CBREC: Hybrid system with both rGO-modified matrix and coated fibers.
     Mechanical properties (tensile, compressive, interlaminar shear, and fracture toughness) were characterized according to ASTM standards to identify the optimal configuration.

2. Multiscale Modeling:

   • Micromechanics: A Representative Volume Element (RVE) approach was employed in ANSYS 2024 R1 to homogenize the effective orthotropic properties of the composites, accounting for the nanoscale reinforcement effects.
   • Macroscale FEM: Nonlinear finite element analysis was conducted using SHELL181 elements to simulate buckling behavior. The model incorporated geometric nonlinearity and progressive damage evolution based on Hashin failure criteria coupled with Continuum Damage Mechanics (CDM).
   • Dataset Generation: A comprehensive dataset of 12,852 laminate configurations was generated by varying geometric parameters (length, width, thickness) and stacking sequences.

3. Physics-Informed Machine Learning:
   To overcome the computational cost of iterative FEA, ML surrogate models were developed using the FEM-generated dataset. Three models were evaluated:

   • Linear Regression (LR) for global linear trends.
   • Support Vector Regression (SVR) for capturing nonlinear stiffness–instability relationships.
   • An Ensemble Model combining LR and SVR (via weighted averaging and stacking) to leverage both linear and nonlinear predictive capabilities.
   • Interpretability: SHapley Additive exPlanations (SHAP) were used to attribute feature importance, ensuring the model's predictions are mechanistically interpretable.

Key Results

• Mechanical Performance: The dual-phase functionalization (CBREC) yielded the most significant improvements. Compared to the control (BEC), the CBREC composite demonstrated a 23.45% increase in tensile strength, a 60% increase in compressive strength (from 200 MPa to 320 MPa), and enhanced interlaminar shear and fracture toughness. These improvements are attributed to synergistic stress distribution, improved interfacial bonding, and increased matrix stiffness.
• Damage Evolution: Progressive damage analysis revealed that the CBREC configuration delays damage initiation and promotes stable load redistribution, effectively mitigating premature failure modes associated with fiber kinking and delamination.
• Machine Learning Performance: The ensemble model achieved a coefficient of determination ($R^2$) of 0.973 in predicting critical buckling loads, significantly outperforming individual models. SHAP analysis identified laminate length and width as the dominant parameters governing buckling resistance.
• Efficiency: The ML surrogate model successfully replaced repetitive FEA simulations, enabling rapid prediction and optimization of buckling performance across the design space.

Significance and Claims
The authors claim that this work represents the first comprehensive experimental-computational investigation demonstrating the role of dual-phase rGO functionalization in enhancing the nonlinear buckling response and progressive damage behavior of basalt fiber-reinforced composites. The study establishes a direct, traceable link between material modification (nanoscale), structural response (macroscale), and data-driven optimization.

The significance of the proposed framework lies in its ability to:

1. Resolve the trade-off between interfacial bonding and matrix toughness through a synergistic dual-phase approach.
2. Provide a physically consistent linkage across scales, translating nanoscale interfacial enhancements into macroscale structural stability predictions.
3. Offer an efficient pathway for the design of lightweight, damage-tolerant composite structures by integrating high-fidelity physics-based modeling with interpretable machine learning, thereby facilitating rapid design exploration without the prohibitive computational cost of full-scale FEA for every iteration.