Arbitrary polygon-based CSFEM-PFCZM for quasi-brittle fracture of concrete

In recent years, engineering and research communities have shown a growing interest in polygon elements due to their adaptability to complex geometries. However, their applicability for investigating the quasi-brittle damage and fracture of concrete structures is still an open question. This work thus develops a numerical framework to integrate the phase-field regularized cohesive zone model (PFCZM) with the cell-based smoothed finite element method (CSFEM) using arbitrary polygon elements. The techniques of centroidal Voronoi tessellation and polytree decomposition are adopted to discretize the computational domains and efficiently refine the potential cracking areas in a multi-level manner. This allows fast transition of the mesh density and direct elimination of the hanging-node issue using the CSFEM. To calculate the displacements and the damage variables, only Wachspress shape functions and boundary geometries are needed, eliminating the need for coordinate mapping and Jacobian inversion. For each CSFEM subcell, crackdriving forces are determined at the integration point and stored as history variables. Typical concrete structures under different loading conditions are validated with respect to the crack path and load-carrying capacity, exhibiting good coarse-mesh accuracy. A mesoscale test-piece under uniaxial tension is also modelled using the developed framework, showing significant computational efficiency when compared to the conventional FEM.