A special purpose Trefftz-element for mode III crack tip loading

A special purpose hybrid Trefftz-element for mode III cracks in thin structures is presented. The element is an extension of well-established mode I/II elements to simulate arbitrary mixed mode loading of a crack. The element formulation is based on analytical solutions of the Kirchhoff plate and exact fulfillment of boundary conditions at the crack edges. Using complex analysis, a T-complete set of homogeneous and particular Ansatz functions is derived. With the particular basis functions a general strip yield model is established and solutions for different distributions of the crack closing force are calculated. Numerical tests of the homogeneous part of the solution are in good accordance with results from high resolution FE simulation. Finally, further extension of the presented element with a kinked crack and a crack propagation algorithm for explicit FE simulations are outlined.