"ECut crack" typically refers to unauthorized versions of the eCut for CorelDRAW plugin, which is used for nesting and CNC G-code generation, often posing security risks. While the term is associated with illegal activation bypasses, authorized versions for professional CNC and laser-cutting are available. For the official installation and activation process, visit e-cut.ru . Download eCut for CorelDRAW
The premature failure at low $E_cut$ is the hallmark of Ecut cracking. The basis set is too small to describe the elongated bonds in the strained lattice. As bonds stretch, the electron density attempts to delocalize, but the rigid low-energy cutoff prevents the inclusion of necessary Fourier components, artificially raising the local energy and causing the bond to snap in the simulation.
This paper addresses a specific failure mode induced by under-convergence, colloquially referred to as "Ecut cracking." This phenomenon occurs when a simulation model subjected to tensile strain fractures prematurely—not due to the physical instability of the material, but due to numerical noise amplified by an insufficient plane-wave basis set. We aim to quantify this effect and establish guidelines to ensure the physical fidelity of simulated mechanical failure.
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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.
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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.
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 $E_cut$.
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To avoid Ecut cracking in mechanical simulations, we propose the following best practices:
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