Modeling of fracture in plates using a Graph-Based Finite Element Analysis (GraFEA)

Abstract

This study is focused on a thermodynamically consistent fracture model for brittle and quasi-brittle plates using a Graph-based Finite Element Analysis (GraFEA) approach. Previous studies (Srinivasa et al., 2021, Thamburaja et al. 2021) formulated a graph-based approach in two and three dimensions, implementing it in Abaqus/Explicit with a vectorized user material subroutine (VUMAT). However, conducting a three-dimensional simulation can be computationally demanding when dealing with thin structures like plates and shells, where the planar dimensions are much larger than the thickness. Hence, in this study, a model based on GraFEA, which describes the deformation kinematics of the plate using the First-order Shear Deformation Theory (FSDT), is proposed. 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 (Srinivasa et al., 2021, Thamburaja et al. 2021). An elastic predictor -fracture corrector method and a velocity-verlet algorithm are used to solve the static and dynamic versions of the governing equations in a finite element framework. 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 observations from the literature at a much lower computational cost. With this model, complex fracture patterns of plates under static and dynamic loading can be simulated in a few minutes on a laptop computer as compared to several hours or days on a supercomputer for a full 3D simulation.