Development of Decoupled Equations Method to Calculate J-Integral in 2D problems

The existence of crack and notch is a significant and critical subject in the analysis and design of solids and structures. As most of damage problems do not have closed-form solutions, numerical methods are current approaches dealing with fracture mechanics problems. This study presents a novel application of the decoupled equations method (DEM) to model crack issues. Based on linear elastic fracture mechanics (LEFM), the J-integral is computed using the DEM. In this method, only the boundaries of problems are discretized using specific higher-order sub-parametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis numerical integration result in diagonal Euler’s differential equations. Consequently, when the local coordinates origin (LCO) is located at the crack tip, the geometry of crack problems are directly implemented without further processing. In order to present infinite stress at the crack tip, a new form of nodal force function is proposed. Validity and accuracy of this method is fully demonstrated through two benchmark problems. The numerical results agree very well with the results from existing experimental results and numerical methods available in literature.