The model of surface nanorelief within continuum mechanics

Grekov, Mikhail A.; Kostyrko, Sergey A.; Vakaeva, Aleksandra B.

doi:10.1063/1.5013743

Cited by 13 publications

(1 citation statement)

References 26 publications

(38 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The development of plastic deformation and fracture processes in these areas determines the mechanical behavior of the material as a whole and is therefore of great interest [1]. The traditional consideration of micro-and nanoscale heterogeneities in the framework of the classical theory of elasticity may lead to inaccuracies in determining the levels of real deformations and stresses [2]- [4].…”

Section: Introductionmentioning

confidence: 99%

Modified Kirsch Problem Incorporating Surface Stresses under Plane Stress

Vakaeva,

Grekov

2023

10th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

View full text Add to dashboard Cite

We consider the Kirsch problem, taking into account the surface stresses at the boundary of the circular hole and on the front surfaces of the plate, in the framework of the original Gurtin-Murdoch model. The boundary conditions on the cylindrical surface of a circular hole in a nanoplate are derived in terms of a complex variable in the case of the plane stress state. The solution of the two-dimensional problem for an infinite plane with a circular hole under remote loading is explicitly obtained. Based on the analytical solution, we investigated the dependence of the elastic stress field on the nanosised plate thickness and dimension of the hole. Numerical examples are given in the paper to illustrate quantitatively the effect of the plate thickness at the nanoscale on the stress field at and near the cylindrical surface. The results are presented graphically as the dependence of the components of the stress tensor on the polar angle.

show abstract

Section: Introductionmentioning

confidence: 99%