# FE-Techniques for Crack Analysis in Linear-Elastic Structures

• Meinhard Kuna
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 201)

## Abstract

The goal of a FEM analysis is the calculation of fracture-mechanical loading parameters for a crack in a structure (test piece, component, material’s microstructure) in the case of linear-elastic (isotropic or anisotropic) material behavior. In Sect. 3.2 the relevant loading parameters of LEFM were introduced: the stress intensity factors $$K_\mathrm{{I}}$$, $$K_\mathrm{{II}}$$, $$K_\mathrm{{III}}$$ and the energy release rate $$G \equiv J$$. Their values depend on the geometry of the structure, its load, the length and shape of the crack and on the material’s elastic properties.

Although FEM can be directly applied to solve a BVP, its use in crack problems involves a fundamental difficulty. This difficulty lies in the exact determination of the singularity at the crack tip with the help of a numerical approximation method such as FEM. Conventional finite element types only have regular polynomial functions for $$u_i$$, $$\varepsilon _{ij}$$ and $$\sigma _{ij}$$. Therefore, they reproduce the crack singularity poorly. For this reason, special element functions, numerical algorithms or evaluation techniques are needed to obtain loading parameters from a FEM solution efficiently and accurately. In the following chapter, we will introduce the methods that have been developed for this, concentrating mainly on stationary cracks. The particularities of FEM techniques and meshes in analyzing unsteady cracks will be dealt with in Chap. 8.

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