A research team led by Yongxing Shen, Associate Dean for Graduate Education at Shanghai Jiao Tong University Global College (SJTUGC, abbreviated as GC), has published a paper in the Journal of the Mechanics and Physics of Solids (JMPS), a flagship journal in solid mechanics. Shen is the sole corresponding author of the paper, titled “Effective fracture toughness for heterogeneous materials accounting for the worst-case scenario.”
High-strength, high-toughness heterogeneous materials are the cornerstone of modern industrial development. Predicting their macroscopic fracture toughness from microstructural features remains one of the key challenges. Existing predictive models often fail to simultaneously account for the complexity and irreversibility of crack propagation paths, the stress criteria for crack initiation, and worst-case conditions in engineering design.
To address these challenges, Shen’s team proposed a computational framework for the anisotropic effective fracture toughness of heterogeneous materials based on the phase-field description of cracks. To approximate the worst-case scenario across all possible translations of a representative volume element (RVE) of the microstructure, the method first determines a specific translation for subsequent analysis. Numerical experiments are then conducted on the translated RVE to simulate tensile loading along a given sampling direction from the initial state to complete fracture. The normalized dissipated energy divided by an appropriate projected area is defined as the effective fracture toughness in that direction. This framework allows for consideration of crack path tortuosity, irreversibility constraints, non-penetration constraints, and stress-based initiation criteria. It can also predict various toughening mechanisms, including toughening induced by ductile inclusions, micro-crack deflection, and strength contrast-induced toughening under uniform fracture toughness conditions.
Schematic of the boundary condition 𝒖=𝑡𝝂 sgn(𝝂 ⋅ (𝒙 – 𝒙c)) on the boundary 𝜕𝛺c. The plane 𝛤v represents the projection of the fracture plane 𝛤 onto the cross-sectional plane normal to 𝝂 in the case of complete fracture.
A solid containing two cases of cracks: (a) a sharp crack; (b) a crack regularized by the phase-field method.
Investigation of the influence of RVE rotation range on the effective fracture toughness under fixed microstructure. The results indicate that RVE rotation has a negligible effect on the effective fracture toughness profile.
First Author Introduction
Sen Liu is a Class of 2025 doctoral graduate of the University of Michigan-Shanghai Jiao Tong University Joint Institute. His research focuses on effective fracture models of heterogeneous materials. He has published papers as first author in Journal of the Mechanics and Physics of Solids and Composite Structures. He received the Best Presentation Award at the International Forum for PhD Students in Mechanics and Interdisciplinary Studies.
Corresponding Author Introduction
Yongxing Shen is the Associate Dean for Graduate Education，a tenured Associate Professor and Doctoral Advisor at Shanghai Jiao Tong University Global College. He received his bachelor’s degree from Tsinghua University and Ph.D. from Stanford University, and previously taught at Universitat Politecnica de Catalunya in Spain. Shen joined the Global College in 2014 and was selected for the national youth talent program. He serves as a young editorial board member of Chinese Journal of Computational Mechanics and was formerly on the editorial board of Chinese Quarterly of Mechanics. His research focuses on computational fracture mechanics and multi-physics coupling problems. He has published more than 60 papers in leading journals, including over 10 in Computer Methods in Applied Mechanics and Engineering and International Journal for Numerical Methods in Engineering.
