Exponential Warping Discretization for Antiplane Crack-Tip Singularities: A Phenomenon of Spurious Smoothing and Its Mechanism

This work reports a numerical phenomenon occurring when an exponential coordinate warping (r = e^{κζ} - 1) is combined with a standard central-difference scheme on a uniform grid. The discrete solution becomes spontaneously smooth at an antiplane shear crack tip, yielding a finite physical stress where the classical solution diverges. The mechanism is identified as a representation failure in the discrete function space. This preprint is positioned as a cautionary note on numerical artifacts near singularities. All code for reproducing the tables is available at the linked repository.