A consistent crack bandwidth for higher-order beam theories: Application to concrete

Higher-order theories have a broad range of successful applications but also suffer from localization instability and mesh-size dependency when modeling quasi-brittle materials such as concrete with strain-softening behavior. To overcome the above difficulties, this paper proposes a fracture energy regularization method with a unified, consistent crack bandwidth specifically tailored for higher-order beam theories. The Carrera unified formulation (CUF) is applied to develop scalable structural theories and related finite elements. To evaluate the accuracy of the new crack bandwidth, three typical experimental quasi-static benchmarks of pure concrete structures are utilized. A modified Mazars damage model with tensile and compressive softening laws is implemented in these benchmarks. The comparison between numerical and experimental results demonstrates that the proposed method can accurately determine the correct crack bandwidth and preserve the dissipated energy per unit area of a fracture surface. Moreover, this robust estimation of crack bandwidth reduces the mesh dependency in general, ensuring the high efficiency of the CUF model.