The extended finite element method in thermoelastic fracture mechanics

Abstract

SUMMARYThe extended finite element method (XFEM) is applied to the simulation of thermally stressed, cracked solids. Both thermal and mechanical fields are enriched in the XFEM way in order to represent discontinuous temperature, heat flux, displacement, and traction across the crack surface, as well as singular heat flux and stress at the crack front. Consequently, the cracked thermomechanical problem may be solved on a mesh that is independent of the crack. Either adiabatic or isothermal condition is considered on the crack surface. In the second case, the temperature field is enriched such that it is continuous across the crack but with a discontinuous derivative and the temperature is enforced to the prescribed value by a penalty method. The stress intensity factors are extracted from the XFEM solution by an interaction integral in domain form with no crack face integration. The method is illustrated on several numerical examples (including a curvilinear crack, a propagating crack, and a three-dimensional crack) and is compared with existing solutions.

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

“…The principle idea of XFEM is shown in Figure 11, simplified for a crack in one dimension. Though XFEM has originally been developed for fracture, it has been extended to numerous applications including two-phase flow [122,123], fluid-structure interaction [124,125], biomechanics [126], inverse problems [127,128], multifield problems [129][130][131][132], among others. XFEM has been incorporated meanwhile into commercial software (XFEM) and has become one of the most popular methods for fracture.…”

Analysis of Thermo-Elastic Fracture Problem during Aluminium Alloy MIG Welding Using the Extended Finite Element Method

“…The SIFs are extracted from the XFEM solution with the help of the crack tip path-independent integrals, which have been extended to the thermal crack problems [10][11][12]15]. The interaction integral method is applied to calculate the SIFs [18].…”

“…Within the framework of thermo-elastic fracture by the XFEM, Duflot [10] investigated the static case of thermo-elastic fracture by XFEM, which considered thermal boundary conditions with different crack faces in both the 2D and 3D problems. Zamani [11] implemented the XFEM to model the effects of mechanical load and thermal shocks on a body with a stationary crack.…”

Analysis and Prediction of Crack Propagation in Plates by the Enriched Free Galerkin Method

“…There are many numerical methods applied for modeling cracks in mechanical problems such as the Boundary Element Method (BEM) [1], the Finite Element Method (FEM) [2], the extended Finite Element Method (XFEM) [3] and Meshless Methods (MMs). Among these methods, the element free Galerkin method and enriched element free Galerkin method has developed by Belytschko et al [4,5] and it has been widely applied in fracture mechanics [6][7][8].…”