Exponential Warping Discretization for Antiplane Crack-Tip Singularities: A Phenomenon of Spurious Smoothing and Its Mechanism
Year: 2026
Type: preprint
Abstract: 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.
Author: Guangheng, Lan
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170047812
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