Early applications of the finite element method to crack problem was
developed by Swedlow and et al. Even though they could get reasonable
accuracy about 5 to 10%, later study showed that solutions in the
vicinity of the crack tip cannot be guranteed to be accurate regardless
of the mesh density around tip. In order to overcome this problem,
people developed special crack tip elements.

In this term paper, I'm going to present 1) Finite Element Method in
Fracture Mechanics and 2) NewFinite Element technique so called Extended Element Method.

In section 1), I am going to develop FEM code for 2D fracture mechanics
problem. First of all, how to develop FEM for fracture. Second, I will
show a simple analysis and compare those result with analytical
solution and commercial software(ABAQUS). Finally, Advantages and
drawbacks of Finite Element Method will be discussed.

In section 2), variety of numerical technique will be introduced with
their benefit and drawbacks. Comparison in FEM and Extended Finite Element Method will be the main story of this topic.

[1] M.H. Aliabadi and D.P. Rooke, Numerical Fracture Mechanics, Comptational Mechanics Publications, 1991
[2] Chungchu Chang, A Boundary Element Method for Two Dimensional
Linear Elastic Fracture Analysis, Dissertation, The University of Texas
at Austin, 1993