Evaluation of stress intensity factors with G-theta method and level sets in Code-Aster

This paper presents an energetic approach to compute mixed mode stress intensity factors (SIFs) along a crack front in linear thermo-elasticity, for meshed or non-meshed cracks. This formulation considers the energy release rate as a symmetric bilinear form of the displacement field and use the explicit expressions of the singular displacements known for a plane strain and anti-plane crack in linear elasticity. We explain how to compute this bilinear form with an extension of the "G-theta" method for a linear thermo-elastic problem in 3D. This method introduces a virtual crack extension velocity field. We focus on how this virtual field is applied on a virtual tore around the crack front. We describe how the discretization and the computation of the energy release rate and the SIFs can be implemented within a general-purpose finite element code. The finite element program Code-Aster®, a free software under GPL license is considered in this study. This approach keeps the advantages of the other methods to determine the SIFs (domain integrals, crack tip contour integrals) without the constraint of an integration box definition, since the formulation is more global. Moreover, the crack is represented by level sets. A local basis at the crack tip can be defined easily within this representation, in which the singular fields can be expressed. This paper includes illustrative examples showing the accuracy of the method. Comparisons with exact solutions prove the efficiency and the robustness of the present formulation for planar crack problems.