A Singular Finite Element on the Mixed-Mode Bimaterial Interfacial Cracks

Abstract

A singular finite element is presented to study the mixed-mode Dugdale-model-based bimaterial interfacial cracks. Firstly, the bimaterial interfacial crack problem is led into the symplectic space, and the symplectic dual equation is obtained and solved analytically. The cohesive stresses of the Dugdale model are treated as special solutions. Subsequently, the analytical solution is employed to develop a novel singular finite element, which depicts accurately the characteristic of displacements and singular stress fields near the crack tip. Finally, combining the singular finite element and conventional finite element method, the length of plastic zone, crack tip opening, and/or sliding displacement can be solved by iteration. Numerical examples are given to illustrate the validity of the present method.

Keywords:

• Singular finite element
• Mixed-mode crack
• Symplectic dual approach
• Interfacial crack
• Dugdale model
• Finite element method

ACKNOWLEDGEMENTS

The work described in this paper was supported by the National Natural Science Foundation of China (No. 10772039), the National Basic Research Program of China (973 Program, No. 2010CB832704), and the National High Technology Research and Development Program of China (863 Program, No. 2009AA044501).