Application II: Solutions of notch and crack problems of one-and two-dimensional quasicrystals

2011 ◽  
pp. 127-157
Author(s):  
Tianyou Fan
Keyword(s):  
Two Dimensional ◽  
Crack Problems

Closed-form solutions of an elliptical crack subjected to coupled phonon–phason loadings in two-dimensional hexagonal quasicrystal media

2018 ◽  
Vol 24 (6) ◽  
pp. 1821-1848 ◽  
Author(s):  
Yuan Li ◽  
CuiYing Fan ◽  
Qing-Hua Qin ◽  
MingHao Zhao
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Elliptical Crack ◽  
Two Dimensional ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Crack Problems

An elliptical crack subjected to coupled phonon–phason loadings in a three-dimensional body of two-dimensional hexagonal quasicrystals is analytically investigated. Owing to the existence of the crack, the phonon and phason displacements are discontinuous along the crack face. The phonon and phason displacement discontinuities serve as the unknown variables in the generalized potential function method which are used to derive the boundary integral equations. These boundary integral equations governing Mode I, II, and III crack problems in two-dimensional hexagonal quasicrystals are expressed in integral differential form and hypersingular integral form, respectively. Closed-form exact solutions to the elliptical crack problems are first derived for two-dimensional hexagonal quasicrystals. The corresponding fracture parameters, including displacement discontinuities along the crack face and stress intensity factors, are presented considering all three crack cases of Modes I, II, and III. Analytical solutions for a penny-shaped crack, as a special case of the elliptical problem, are given. The obtained analytical solutions are graphically presented and numerically verified by the extended displacement discontinuities boundary element method.

The Dirichlet-to-Neumann map for two-dimensional crack problems

2011 ◽  
Vol 200 (9-12) ◽  
pp. 1263-1271 ◽  
Author(s):  
Dorinamaria Carka ◽  
Mark E. Mear ◽  
Chad M. Landis
Keyword(s):  
Two Dimensional ◽  
Crack Problems ◽  
Dirichlet To Neumann Map

scholarly journals An interaction integral method for evaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method

2015 ◽  
Vol 18 (2) ◽  
pp. 106-113
Author(s):  
Nha Thanh Nguyen ◽  
Hien Thai Nguyen ◽  
Minh Ngoc Nguyen ◽  
Thien Tich Truong
Keyword(s):  
Integral Method ◽  
Interpolation Method ◽  
Two Dimensional ◽  
Radial Point Interpolation Method ◽  
Interaction Integral ◽  
Crack Problems ◽  
Radial Point Interpolation ◽  
T Stress ◽  
Point Interpolation Method ◽  
Point Interpolation

The so-called T-stress, or second term of the William (1957) series expansion for linear elastic crack-tip fields, has found many uses in fracture mechanics applications. In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. The T-stress can be calculated directly from a path independent interaction integral entirely based on the J-integral by simply the auxiliary field. Several benchmark examples in 2D crack problem are performed and compared with other existing solutions to illustrate the correction of the presented approach.

Numerical Study on Two-Dimensional Crack Problems in Three-Layered Isotropic Elastic Materials

2006 ◽  
Vol 312 ◽  
pp. 53-58
Author(s):  
Xi Zhang ◽  
Rob Jeffrey
Keyword(s):  
Numerical Study ◽  
Layered Material ◽  
Displacement Discontinuity ◽  
Image Method ◽  
Displacement Discontinuity Method ◽  
Two Dimensional ◽  
Governing Equations ◽  
Crack Problems ◽  
Distributed Dislocation ◽  
Dislocation Technique

Two-dimensional crack problems in a three-layered material are analysed numerically under the conditions of plane strain. An image method is proposed to obtain a fundamental solution for dislocation dipoles in trilayered media. The governing equations can be constructed by distributed dislocation technique and the solutions are sought in terms of the displacement discontinuity method. Comparisons are made between existing results in the literature and numerical results for different cases and good agreements are found.

D-24 Analysis of two-dimensional crack problems by mesh-free Body Force Method

2016 ◽  
Vol 2016.69 (0) ◽  
pp. 171-172
Author(s):  
Ryosuke HONDA ◽  
Akihide SAIMOTO ◽  
Yohei SONOBE ◽  
Konatsu TOMINAGA
Keyword(s):  
Body Force ◽  
Two Dimensional ◽  
Force Method ◽  
Body Force Method ◽  
Mesh Free ◽  
Crack Problems ◽  
Free Body

Evaluation of Fracture Toughness of Ceramic-Metal Functionally Graded Materials

2010 ◽  
Vol 123-125 ◽  
pp. 971-974
Author(s):  
Sheikh Md. Rasel ◽  
Foisal Ahmed Mirza ◽  
Ali Md. Afsar ◽  
Jung I. Song
Keyword(s):  
Compressive Load ◽  
Functionally Graded ◽  
Correlation Technique ◽  
Two Dimensional ◽  
Graded Materials ◽  
Three Point Bending ◽  
Initiation And Propagation ◽  
Crack Problems ◽  
Growth Initiation ◽  
Model Crack

The main objective of this study is to examine the two dimensional surface crack problems in a system with an interface between two elastic-plastic solids of different yield strength subjected to mode I mechanical loading. The surface cracks growth is considered to occure along the interface direction of bimaterials which is perfectly bonded to each others. A two dimensional finite elementmethod is used to solve the structural problem. Solid 183-node elements are utilized to simulate the strain singularity around the crack front. The crack surface is subjected to a compressive load by three point bending. The stress intesity factors are computed by using the displacement correlation technique. The primary goal is to develop a model crack tip stresses and strains in a manner that is useful for crack growth initiation and propagation in a FGM.

Sign in / Sign up

Export Citation Format

Share Document