Modeling of fracture in brittle and quasi-brittle materials using graph-based finite element approach

A thermodynamically consistent model for modeling fracture in brittle and quasi-brittle plates is presented.In particular, using the graph-based (GraFEA) approach of the authors to model fracture in two and three-dimensional elastic problems, a GraFEA model that describes the bending kinematics of plates using the first-order shear deformation theory (FSDT) is developed.The fundamental idea of this model is the presence of multiple microcrack planes traversing through a material point on the top and bottom surfaces of the plate.The state of a crack plane evolves based on the probabilistic description of microcracks at the top and bottom half of the plate.An elastic correctorfracture predictor method and a velocity-verlet algorithm are used to solve the equations governing the bending of plates.It is shown that the proposed formulation compares well with the numerical results from the GraFEA 2D and GraFEA 3D simulations as well as experimental results found in the literature.Complex fracture patterns of plates under static and dynamic loads are predicted within a few minutes on a laptop computer as compared to several hours or days on a supercomputer for a full 3D simulation.A number of numerical examples of plate bending are presented to show the model's robustness.