Reduced order mathematical homogenization method for polycrystalline microstructure with microstructurally small cracks

• Published in: International journal for numerical methods in engineering Vol. 124; no. 14; pp. 3166 - 3190
• Main Authors: Xia, Damin, Oskay, Caglar
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.07.2023; Wiley Subscription Services, Inc
• Subjects: computational homogenization; Crack tips; Cracks; crystal plasticity; Homogenization; Mathematical analysis; microstructurally small cracks; Microstructure; Model reduction; Plastic deformation; Polycrystals; reduced order modeling; Reduced order models; Stress distribution
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.7243

In this manuscript, a reduced order homogenization model is developed for polycrystalline microstructures with microstructurally small cracks. The proposed approach employs and advances the eigendeformation‐based homogenization method to account for the plastic deformation within the microstructure and the presence of cracks. A novel approach to construct the reduced order basis for the separation field is proposed for approximating crack opening profiles of kinked cracks. To capture the variable stress fields around the crack tips, a domain partitioning strategy that automatically refines the reduced order parts in these regions is proposed. The model performance is evaluated against reference crystal plasticity finite element (CPFE) simulations under various loading conditions and crack configurations. Both the overall and local response predictions show reasonable accuracy with only a fraction of the computational cost of the reference simulations.