Hello, I am making mesh on semi elliptical crack in Abaqus. The problem is that to make mesh perpendicular to crack front I have to make partition at the face of crack. I am following Neuman and Raju's strategy where they transformed semi circular crack to elliptical crack and the corresponding radial lines to hyperbolas. In tis way we can get the perpendicular meshes at crack front. I know how to transform circle into ellipse but I am not sure how to transform radial lines into hyperbolas. I am attaching a picture of what I wanted to do. If any one know the answer please let me know. I have been trying for months now.