Explicit Phase-Field Regularized Voronoi-Based Lattice Model for Quasi-Brittle Fracture and Its Finite Element Implementation

In this study, the conventional Voronoi-based irregular lattice model is regularized by the phase-field method, which effectively introduces a characteristic length parameter to overcome the mesh-size dependent solution. To circumvent the local instability (snap-back) which generally requires sophisticated arc-length control, the so-called phase-field regularized Voronoi-based lattice ( PHL ) model is realized using an explicit finite element solver. Furthermore, the constitutive law of quasi-brittle materials is embraced when establishing the PHL model, which is proven length-scale insensitive. We show that the PHL model with an explicit solver is very robust and computationally efficient, provided with proper parameters and parallel computing. Moreover, the necessary fine mesh size in the implicit phase-field method is greatly released in the explicit PHL model, of which accurate results could be obtained with the coarser mesh size. Several experiments are adopted to demonstrate the model, including the size effect and mix-mode bending of concrete specimens. Cracks’ initiation, propagation, and coalescence could be automatically captured without any tracking algorithms. In addition, it is noteworthy that the model could easily be extended to coupled mechanical and transportation problems.