Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0201045

Size Effect in Fracture: Roughening of Crack Surfaces and Asymptotic Analysis

S. Morel·E. Bouchaud·G. Valentin
View original source ↗Read source document ↗Export metadata ↓

Abstract

Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis allows to extend the link to the nominal strength of structures. We show that a Family-Vicsek scaling leads to the classical size effect of linear elastic fracture mechanics. On the contrary, in the case of an anomalous scaling, there is a smooth transition from the case of no size effect, for small structure sizes, to a power law size effect which appears weaker than the linear elastic fracture mechanics one, in the case of large sizes. This prediction is confirmed by fracture experiments on wood.

Explore related subjects

cond-mat.mtrl-sci

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. Morel, E. Bouchaud, G. Valentin. 2002-01-04. Size Effect in Fracture: Roughening of Crack Surfaces and Asymptotic Analysis. https://doi.org/10.1103/physrevb.65.104101

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Coexistence of Donor and Acceptor Hydrogen States in n-Type InN

Hydrogen often exhibits amphoteric behavior in semiconductors, but its role is in n-type InN remains unresolved. Wurtzite InN is a narrow-gap semiconductor with high electron mobility and is therefore attractive for high-speed electronics and optoelectronic applications. Here we use hard x-ray photoemission spectroscopy (HAXPES) to probe hydrogen-related electronic structure in as-grown and post-annealed InN thin films prepared at different grown temperatures. Post annealing, which reduces the concentration of hydrogen impurities in the films, shifts the core-level spectra toward lower binding energy, consistent with a chemical-potential shift associated with the passivation of electron carriers. In the valence-band spectra, an acceptor-like in-gap feature near the valence-band maximum is suppressed after annealing. Together with the established donor-like behavior of hydrogen in InN, these results suggest that acceptor H- states coexist with donor H+ states in InN. The coexistence of these opposite hydrogen charge states provides a microscopic picture of hydrogen-driven compensation in InN and highlights the amphoteric nature of hydrogen even in a highly n-type semiconductor.

cond-mat.mtrl-sci↗
arXiv2026

Updated Tkatchenko Scheffler method and assessment of dispersion methods for alkali-containing systems

The Tkatchenko-Scheffler (TS) pairwise method to calculate dispersion interactions is a widely used approach to incorporate missing long-range van der Waals contributions in semilocal and hybrid density functional calculations. Despite subsequent many-body extensions, this formulation remains widely used. In 2018, Fedorov et al. reported updated van der Waals radii to the seminal work published in 2009. The present work examines the accuracy of the TS method with updated van der Waals radii (TS_2018), coupled with the semilocal Perdew-Burke-Ernzerhof density functional, for structural predictions of semiconducting and insulating materials. Special attention is paid to materials containing alkali elements, for which the TS_2009 method exhibits a large overbinding, associated with potentially large errors in predicted atomic structures. We also consider a narrower reformulation (TS_alkali) where only the the alkali atoms are corrected, so the method remains otherwise compatible with TS_2009. We compare these methods with a broader set of dispersion corrections--the DFT-D3 method, the exchange-hole dipole moment method, and the beyond-pairwise, nonlocal many-body dispersion method--for ionic and alkali-containing systems more generally. We examine equilibrium geometry predictions for 45 inorganic solid compounds as well as three Cs-containing halide perovskites, CsPb$X_3$ ($X$ = Cl, Br, I). Our results show that the updated van der Waals radii in the TS_2018 and TS_alkali methods resolve the overbinding that is present with TS_2009 in alkali-containing systems, bringing predictions into closer agreement with other dispersion methods. For the halide perovskites, method-dependent differences in predicted cell volumes and shapes persist, and no approach performs with perfect accuracy on all metrics for all three materials.

cond-mat.mtrl-sci↗
arXiv2026

Hierarchical Fourier Phase Projection for Local Electronic Observables

In this letter, we develop hierarchical Fourier phase projection (HPP) for the calculation of local electronic observables. The method couples the spatial decay of the density matrix with a hierarchy of Fourier probes, improving accuracy through refinement, and making use of all previously evaluated responses. The variation in the calculated observables during the refinement process carries information on the residual error. We use a locality-based model to estimate the error from these changes with no extra probing calculations. In particular, we demonstrate the method for electron densities and nonlocal pseudopotential forces for fixed Kohn-Sham Hamiltonians of semiconductors, metals and thermally perturbed silica. The convergence is significantly accelerated by the spatial decay of the density matrix, especially if the density matrix is short-ranged. The number of probes necessary to achieve a specific local accuracy is only weakly dependent on the system size within the range of consideration. HPP provides a route toward linear-scaling electronic-structure calculations in which the computational effort for local observables can be matched to the required accuracy, offering an error-aware strategy for large-scale first-principles simulations.

cond-mat.mtrl-sci↗