Molecular Dynamics Calculations of Asymptotic Series Coefficients for Stress Fields

This paper presents an overdeterministic algorithm for constructing the asymptotics of the stress field near the tip of a nanocrack in an anisotropic linear elastic body with cubic symmetry. A molecular dynamics solution of the problem of mixed loading (mode I fracture and transverse shear) of singl...

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Veröffentlicht in:Journal of applied mechanics and technical physics Jg. 66; H. 2; S. 350 - 364
Hauptverfasser: Mushankova, K. A., Stepanova, L. V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.04.2025
Springer Nature B.V
Schlagworte:
Algorithms
Aluminum
Anisotropic media
Applications of Mathematics
Approximation
Asymptotic series
Classical and Continuum Physics
Classical Mechanics
Compliance
Copper
Crack tips
Deformation
Elastic anisotropy
Elastic bodies
Elastic deformation
Exact solutions
Fluid- and Aerodynamics
Fracture mechanics
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mechanical Engineering
Mechanical properties
Molecular dynamics
Physics
Physics and Astronomy
Single crystals
Stress distribution
Symmetry
Tensors
Transverse shear
Visualization
anisotropic medium
cubic symmetry of elastic properties
molecular dynamics method
atomistic stresses
ISSN:0021-8944, 1573-8620
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Zusammenfassung:This paper presents an overdeterministic algorithm for constructing the asymptotics of the stress field near the tip of a nanocrack in an anisotropic linear elastic body with cubic symmetry. A molecular dynamics solution of the problem of mixed loading (mode I fracture and transverse shear) of single-crystal copper and aluminum nanoplates with a central cut is described. Based on this solution, an asymptotic representation for the stress tensor components was derived. The atomistic stresses in the vicinity of the crack tip were calculated, and the coefficients of the series representing the stress field were determined using the values of the atomistic stress tensor components. The molecular dynamics calculations were performed for a temperature of 10 K to exclude the occurrence of nonlinear elastic deformation near the crack tip. The stress fields in the atomistic and analytical solutions were compared. The stresses at different distances from the nanocrack tip are in good agreement with the solutions of problems of classical macroscopic theory of anisotropic elasticity and can be described using a series that extends the Williams series to anisotropic media. In the series extended to anisotropic materials, the regular (nonsingular) terms are taken into account and the series coefficients of these terms are determined. It is shown that the developed algorithm can be used to effectively determine the coefficients of the higher-order terms of the series.
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ISSN:0021-8944
1573-8620
DOI:10.1134/S0021894425020166