Precise computation and error control of stress intensity factors and certain integral characteristics in anisotropic inhomogeneous materials

The numerical simulation of quasi-static crack propagation is closely related to the computation of characteristics such as stress intensity factors or energy release rates. In this work, ideas are proposed, how such quantities can be calculated precisely in linear elastic, anisotropic and inhomogeneous plane structures. Stress intensity factors and other local characteristics can be evaluated in terms of functionals depending on solutions of certain elasticity problems. The approach used here to calculate these functional values precisely with Galerkin finite elements is a dual-weighted-residual method for adaptive mesh refinement and a posteriori error control. Especially in structures under mixed-mode loadings contact of crack faces can occur. A numerical realization of mutual non-penetration conditions of inequality type for the crack faces and the effect of such constraints on stress intensity factors is shown. Numerical results are presented for anisotropic and functionally graded materials.