Simulation of 2D linear crack growth under constant load using GFVM and two-point displacement extrapolation method

Abstract

• A novel GFVM formulation is introduced for modeling 2D irregular crack propagation . • Unstructured GFVM is useful to solve crack propagation in geometrically complex structures. • Matrix free GFVM reduces computation time of iterative or time-dependent solutions. • Linear GFVM produces accurate results near the crack, where small elements are needed. A new approach to model two-dimensional linear crack propagation, based on the Galerkin Finite Volume Method (GFVM), is proposed. The displacement field is calculated using the GFVM method by solving two-dimensional equilibrium equations on an unstructured triangular mesh. An essential feature of this method is that it does not require matrix operations; hence, it obviously reduces computation time. The Two-Point Displacement Extrapolation (TPDE) technique is employed to calculate Stress Intensity Factors (SIFs). The accuracy of the structural solver that has been developed is evaluated using five test cases. In the first example, a Timoshenko cantilever beam, carrying an end point load, is analyzed. In the second and third examples, stress intensity factors are computed for edge and inner crack development in plates under transient loading. The GFVM results are then compared with their counterparts that resulted from the Explicit Finite Element Method (E-FEM). The comparison indicates that the FVM has an accuracy close to E-FEM, whereas the FVM drastically reduces the computational time. A case study is conducted to simulate the gradual propagation of crack. The results computed by the numerical simulation presented are in excellent agreement with the corresponding results from the analytical solution as well as experimental measurements.