Crack propagation in quasi-brittle materials by fourth-order phase-field cohesive zone model

A phase-field approach becomes a more popular candidate in modeling crack propagation. It uses scalar auxiliary variable, namely to model discontinuity zone continuity domain. Furthermore, the fourth-order produces better convergence rate and accurate solutions than second-order one. However, it is available for propagation brittle material. This study addresses combining non-standard form with cohesive (CZM) predict quasi-brittle Cornelisson's softening law used capture high precision of prediction. The concrete material considered as For computation efficiency using NURBS-based finite elements, Virtual Uncommon-Knot-Inserted Master-Slave (VUKIMS) technique employed derive local refinement mesh. Numerical results are verified by published ones from literature. was found that peak load path independent element size insensitive length-scale number CZM. Our proposed shows most significant advantage compared standard terms computational cost solution accuracy.