Prof Eckart Schnack from the Institute of Solid Mechanics at Karlsruhe University (Germany), delivered a lecture on Friday 3 July 2009 entitled “Discussion of experimental data for 3D crack propagation on the basis of 3 dimensional singularities”. He presented an algorithm for high precision computations of eigenvalues characterising singularities near re-entering corners or wedges in isotropic elastic 3D bodies. Singularities have been calculated on the basis of application of the Kondratiev’s theorem for elliptical boundary value problems. The algorithm also assumes the application of the Petrov-Galerkin finite element method to the problem involving both the Dirichlet and Neumann boundary conditions. The algorithm is iterative and implements the Arnoldi method to determine the dominant singularity exponent. In addition, some new formulations for 3D crack propagation problems have been considered in order to take account of the curvature of the crack surface.
The algorithm has been applied to simulate fracture propagation in typical experiments on bending that were conducted by the Prof Schnak’s colleagues at the University of Erlangen - Nuremberg. Good agreement between simulations and experiments has been reported for different samples with growing cracks.
The lecture stimulated a lively discussion on the topic.
Wessex Institute