Applied Mathematics and Mechanics

, Volume 20, Issue 2, pp 143–153

# The analysis of crack problems with non-local elasticity

• Zhao Minghao
• Cheng Changjun
• Liu Guoning
• Shen Yapeng
Article

## Abstract

In this paper, the displacement discontinuity fundamental solutions (DDFS) corresponding to the unit concentrated displacement discontinuity for plane problems of non-local elasticity are obtained. Based on the displacement discontinuity boundary integral equation (DDBIE) and boundary element method (BEM), a method of analysis of crack problems in non-local elasticity with generalized purpose is proposed. By using this method, several important problems in fracture mechanics such as edge crack are studied. The study of edge crack shows that the stress concentration factor (SCF) near the crack tip is not a constant but varies with the crack length. With this result the effect of crack length on the fracture toughness K I c is studied. The results obtained in this paper are in accordance with the published ones.

### Key words

crack boundary integral equation (BIM) boundary element method (BEM) non-local elasticity fundamental solution

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© Editorial Committee of Applied Mathematics and Mechanics 1999

## Authors and Affiliations

• Zhao Minghao
• 1
• Cheng Changjun
• 2
• Liu Guoning
• 1
• Shen Yapeng
• 3
1. 1.Zhengzhou Research Institute of Mechanical EngineeringZhengzhouP R China
2. 2.Department of MechanicsShanghai University; Shanghai Institute of Applied Mathematics and MechanicsShanghaiP R China
3. 3.Xi'an Jiaotong UniversityXi'anP R China