A phase-field cohesive zone model integrated with cell-based smoothed finite element method for quasi-brittle fracture simulations of concrete at mesoscale

In this work, a phase field cohesive zone model (PFCZM) combined with the cell-based smoothed finite element method (CSFEM) is presented to investigate the quasi-brittle fracture behaviour of concrete at mesoscale. An automatic quadtree decomposition technique is employed to discretise the CT image-based meso-structures including aggregates, mortar and pores, with local mesh adaptively refined at material boundaries. The resultant quadtree elements with hanging nodes are naturally treated as CSFEM polygons. In the proposed CSFEM-PFCZM, the stiffness matrices and residual vectors for displacement and damage fields are formulated by the Wachspress shape function and smoothed strain matrices. The crack driving forces are evaluated as history variables at the integration points of CSFEM subcells. Four nonlinear fracture benchmarks are presented to validate the proposed method regarding the variability of mesoscale fracture processes, crack topology and load–displacement curves. It is found that the CSFEM-PFCZM combined with the quadtree decomposition significantly improves the computational efficiency over the traditional FEM counterparts, and shows great potential for multiscale fracture evaluation of quasi-brittle composite materials. This is due to the fast mesh generation and flexible simulation of complicated nonlinear fracture using the CSFEM-PFCZM without the need for remeshing or mesh enrichments.