This paper highlights the critical impact of plane-wave cutoff energy on the simulation of mechanical failure. "Ecut cracking" is a numerical artifact where insufficient basis set size induces premature, unphysical fracture. This phenomenon arises from the inability of a restricted basis set to accommodate electron density changes during bond stretching, exacerbated by Pulay stress effects. Our results demonstrate that conventional energy-based convergence testing is insufficient for fracture mechanics simulations. Robust mechanical modeling requires rigorous convergence testing of the stress tensor to ensure that the observed cracking reflects the material's physics, rather than the limits of the computational basis set.
In DFT, the Kohn-Sham orbitals $\psi_n,\mathbfk$ are expanded as a linear combination of plane waves: $$ \psi_n,\mathbfk(\mathbfr) = \sum_\mathbfG c_n,\mathbfk(\mathbfG) e^i(\mathbfk+\mathbfG)\cdot\mathbfr $$ where $\mathbfG$ is a reciprocal lattice vector. The summation is truncated such that the kinetic energy $\frac\hbar^22m|\mathbfk+\mathbfG|^2$ does not exceed the cutoff energy $E_cut$.
In computational materials science, Density Functional Theory (DFT) serves as the bedrock for predicting material properties. However, the accuracy of these predictions is intrinsically linked to numerical convergence parameters, most notably the plane-wave kinetic energy cutoff ($E_cut$). This paper investigates the phenomenon of "Ecut cracking"—a term describing the spurious mechanical failure or structural instability observed in simulations employing insufficient cutoff energies. Through a systematic analysis of bulk silicon and alpha-quartz, we demonstrate that low $E_cut$ values introduce artificial stress inhomogeneities and erroneous bond stiffness, leading to unphysical fracture initiation at stress levels significantly below experimental values. We propose a protocol for $E_cut$ convergence testing specifically tailored for mechanical property calculations to prevent these numerical artifacts. ecut crack
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Figure 1 (hypothetical) displays the stress-strain curves for Silicon. The summation is truncated such that the kinetic
To avoid Ecut cracking in mechanical simulations, we propose the following best practices:
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