A Substructuring Homogenization Model for Efficient Fracture Analysis in Perforated Plates
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This research presents a high-efficiency computational framework for simulating crack propagation in periodic perforated square plates by leveraging a multi-scale substructuring strategy. The primary objective was to establish a robust Representative Volume Element (RVE) based homogenization procedure to predict effective orthotropic elastic properties without the need for traditional, complex theoretical derivations. Using the finite element (FE) method in conjunction with periodic boundary conditions (PBCs), the equivalent material constants of the perforated domain were determined, ensuring displacement and traction continuity across the unit cell boundaries. To evaluate the reliability of the RVE-based homogenization, tension test simulations were conducted and compared. The homogenized model demonstrated high accuracy, with the error in predicted stiffness values being only 1%. Additionally, the approach significantly improved computational efficiency, reducing the CPU time by approximately 50% compared to the explicit model. The core contribution of this work is the integration of these homogenized properties into a fracture mechanics framework using domain substructuring. In this hybrid model, the region immediately surrounding the crack path retains its explicit perforated geometry to accurately capture local stress concentrations and crack-tip singularities. Conversely, the bulk of the plate is modeled as a homogenized orthotropic medium. This dual-domain approach effectively reduces the overall computational overhead while maintaining the fidelity required for fracture analysis.
