Numerical simulation of localized quasi-brittle fracture with an enhanced bi-energy norm based equivalent strain

This paper presents an improved local continuum damage model for quasi-brittle fracture analysis. A local damage model, as compared to its non-local damage counterpart, owns the advantages of simple implementation and low computational cost. However, it is in general suffered from the mesh-size dependency. In this work, this drawback is mitigated by incorporation of fracture energy and element characteristic length into the evaluation of damage parameter. For estimation of the equivalent strain, the concept of bi-energy norm, which allows the quantification of contribution from tension and compression parts of strain, is further enhanced by incorporation of the equivalent strain for cracking and crushing based on Mazars damage concept. The purpose of introducing this new incorporated bi-energy norm aims to improve the ability to simulate mixed-mode fracture behavior. The performance and accuracy of the developed local damage approach in modeling quasi-brittle fracture is illustrated through several numerical examples. The structural displacement-force curves and crack patterns are analyzed and compared with experimental data and reference numerical solutions derived from other numerical methods. In particular, as compared to the original bi-energy norm, numerical results indicate that our enhanced bi-energy norm based equivalent strain can predict better crack path of Nooru-Mohamed's test for double-edge notched concrete specimen.

Automated summary

This paper proposes an improved local continuum damage model for analyzing quasi-brittle fracture. The model incorporates fracture energy and element characteristic length to mitigate the mesh-size dependency issue. The enhanced bi-energy norm and equivalent strain are used to simulate mixed-mode fracture behavior. Numerical examples demonstrate the accuracy and effectiveness of the developed local damage approach in modeling quasi-brittle fracture, especially in predicting crack paths.