Martin Steigemann

Crack propagation in anisotropic composite structures

A crack approaching a material interface between two elastic materials may stop or may advance by either penetrating the interface or deflecting into the interface (cf. N.Y. He and J.W. Hutchinson, Int. J. Solids Struct. 25 (1989), 1053-1067). Mathematical models for crack path prediction are based on the asymptotic behavior near the crack tip. In this work, an idea to compute the asymptotic expansion of the displacement field for structures composed of two dissimilar elastic anisotropic materials is shown, if the crack impinges the material interface. In contrast to the well-known case of isotropic materials, logarithmic terms can appear in the asymptotic decomposition of the displacement field in anisotropic composites. Based on this results, the energy release rate is calculated for different scenarios of crack propagation in composite structures.

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.