When simulating cohesive cracks in the XFEM framework, specific enrichment schemes are designed for the non-singular near-tip field and an iteration procedure is used to solve the nonlinearity problem. This paper focuses on convergence and accuracy analysis of XFEM enrichment schemes for cohesive cracks. Four different kinds of enrichment schemes were manufactured based on the development of XFEM. A double-cantilever beam specimen under an opening load was simulated by Matlab programming, assuming both linear and exponential constitutive models. The displacement and load factors were solved simultaneously by the Newton–Raphson iterative procedure. Finally, based on a linear or an exponential constitutive law, the influences of variations in these enrichment schemes, including (i) specialized tip branch functions and (ii) corrected approximations for blending elements, were determined and some conclusions were drawn.

The present paper aims to study the crack propagating behavior of a stiffened plate under tensile and bending displacement load loads. The extended finite element method (XFEM) is used to analyze the residual ultimate strength of stiffened plates with a central crack. The quasi-static crack growth process is simulated by software ABAQUS. The validity of the grid is validated by the plate with a central crack. The numerical method is validated by comparing the fatigue crack growth rate of the round compact tension specimen (RCT) results of the extended finite element with experiment values. Influential parameters, including the size of the stiffened plates, heights of the stiffeners is varied, and uniaxial tensile and four-point bending models are analyzed. The results show that ultimate strength is reduced by the action of tensile and bending loads. The bottom plate and stiffener are destroyed with crack propagation, successively. With the increase in stiffener height, the crack resistance will also increase, thus restraining the central crack growth of stiffened plates.

In this study, the extended finite element method (XFEM) was integrated into the generalized multiscale finite element method with global–local enrichment (GFEM^gl) to simulate 2D heat conduction in highly heterogeneous materials (i.e., matrixes with numerous randomly distributed inclusions or voids). This multiscale scheme was used to evaluate the effective thermal conductivity (ETC) of composites through simulation based on a representative volume element (RVE). In the proposed method, global–local enrichments are numerically constructed and incorporated into the global approximation in a hierarchical manner to integrate microstructure information into the macroscale problem. The XFEM is employed on a microscale mesh to avoid using a conformal mesh. RVEs containing numerous inclusions or voids with different volume fractions were numerically simulated using the proposed multiscale method, and the obtained results were compared with those of the standard single-scale XFEM and analytical models. The simulation results indicated that the proposed method has excellent accuracy and considerably lower computational cost.

The link of fracture analysis of large ships is an essential part of the structural safety of ships. However, the finite element analysis of large structure according to the traditional method not only has high requirements on the computer, but also the influence of the mesh encryption at special locations makes further requirements on the accuracy of the ship. In this paper, based on the extended finite element method (XFEM) and the multi-point constraint method (MPC), the dynamic crack expansion process of the rectangular plate containing cracks under the multi-scale model is comparatively studied by using ABAQUS simulation software Finally, the applicability of the method is verified by applying the multi-scale model of ship nodes. The results show that the computational effort of the multi-scale model is significantly reduced with the same accuracy and allowable error, which proves the accuracy and efficiency of the method.