About cracks, dunce caps and a new way to stop cracks

Recently, the 'method of tensile triangles' has been introduced for optimizing the shape of notches by adding material at overloaded regions but also to remove unloaded material from an oversized design proposal.
In this work, we apply the method to demonstrate that the unloaded region in the vicinity of a crack has the shape of spindle-shaped hole, which looks like two dunce caps mirrored at the crack line. Also, these shapes can be predicted by the 'method of tensile triangles' without any FEM-effort. Furthermore, we show a new way to stop cracks by deviating the crack tip into a shape-optimized pattern leading to a compressive stress that closes the crack tip. This procedure is now used in chemical engineering.