Subdomain-based error techniques for generalized finite element approximations of problems with singular stress fields

2013 ◽  
Vol 52 (6) ◽  
pp. 1395-1415 ◽  
Author(s):  
Felício B. Barros ◽  
Clovis S. de Barcellos ◽  
C. Armando Duarte ◽  
Diego A. F. Torres
Keyword(s):  
Finite Element ◽  
Stress Fields ◽  
Singular Stress ◽  
Finite Element Approximations ◽  
Singular Stress Fields ◽  
Generalized Finite Element

Computations of Singular Stresses Along Three-Dimensional Corner Fronts by a Super Singular Element Method

2017 ◽  
Vol 14 (06) ◽  
pp. 1750065 ◽  
Author(s):  
Xuecheng Ping ◽  
Mengcheng Chen ◽  
Wei Zhu ◽  
Yihua Xiao ◽  
Weixing Wu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Stress Fields ◽  
Singular Element ◽  
Singular Stress ◽  
Numerical Studies ◽  
Enriched Finite Element ◽  
Singular Stress Fields

In order to consider corner configurations with straight corner fronts in three-dimensional (3D) solids, a super polygonal prismatic element containing a straight corner front is established by using the numerical eigensolutions of singular stress fields and the Hellinger–Reissner variational principle. Singular stresses near the corner front subject to far-field boundary conditions can be obtained by incorporating the super singular element with conventional 3D brick elements. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture problems of 3D corner configurations and cracks. The usage of the super singular element can avoid mesh refinement near the corner front domain that is necessary for conventional and enriched finite element methods, and lead to high accuracy and fast convergence. Compared with the conventional finite element methods and existing analytical methods, the present method is more suitable for dealing with complicated problems of stress singularity in elasticity including multiple defects.

The detachment of an inclined micro-pillar adhered to a dissimilar substrate

2021 ◽  
pp. 1-22
Author(s):  
Nitish Kumar ◽  
Syed Nizamuddin Khaderi
Keyword(s):  
Stress Intensity ◽  
Axial Load ◽  
Interfacial Crack ◽  
Axial Loading ◽  
Stress Fields ◽  
Singular Stress ◽  
Elastic Mismatch ◽  
Bending Loads ◽  
Singular Stress Fields ◽  
The Moment

Abstract We investigate the mechanics of the detachment of an inclined micro-pillar adhered to a dissimilar substrate when subjected to a combination of an axial load and end moment. When the micro-pillar has adhered to the substrate, singular stress fields exist at the bi-material corners. The order of singularity is estimated using asymptotic analysis. The first two terms in the asymptotic expansion lead to singular stress fields. The magnitude of the singularity is evaluated in terms of the elastic mismatch between the pillar and substrate and the micro-pillar inclination. The asymptotic stress due to the moment loading is more sensitive to the micro-pillar inclination when compared to that due to the axial loading. They are insensitive to the micro-pillar inclination when the micro-pillar is rigid when compared to the substrate. A short interfacial crack is further assumed to exist at the bi-material corner. This crack is embedded in the corner singularity region and is loaded by the singular fields due to axial and bending loads. A boundary layer analysis is performed on the singular zone to estimate the stress intensity factor when a short crack embedded in it is subjected to the singular fields. The stress intensity factors are also calculated for a long interfacial crack at the bi-material corner, which extends beyond the singular zone. Using the above results, we investigate the detachment of the inclined micro-pillar under the combination of an axial load and end moment.

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