عنوان مقاله [English]
This study investigates stress components in the extended finite element method for the standard and enriched degree of freedom. The stress components for the enriched degree of freedoms are developed, and conventional stress components of the standard degree of freedoms are modified. Numerical integration of the restoring forces equations leads to these new stress formulations. So, new polynomial functions are developed by eliminating the element partitioning when the shifted Heaviside function is utilized. The force convergence criterion verifies the proposed stress formulas. The new stress formulation's added terms seem to simulate the effects of discontinuity within the cracked body. The suggested formulations for the standard degree of freedom reduce stress contours in the cracked elements. And, the regions with high stresses represent the candidate elements for cracking in the next load steps. The conventional stress algorithm is not consistent with the crack propagation process inside the body because these stresses are higher than the material's tensile strength at the cracked regions. Additionally, the proposed stresses for the standard DOFs have unique values at the whole domain of the cracked elements, indicating the entire domain status. It is shown that the stress components for the enriched DOFs represent the tractions at the crack faces, although properties of nonlinear material behavior are not considered. It is proven that the internal forces calculated utilizing the proposed formulation are in equilibrium with the external loads. Furthermore, it is shown that investigating the restoring forces and their slopes give a good judgment of the process in which the element loses its ability to withstand the imposed loads. The higher the slopes of the restoring forces for the standard DOF are, the healthier the body is, and it has more ability to withstand the applied loads. Moreover, abrupt changes of the restoring forces indicate the cracking in adjacent elements.