3D Crack Problems Research Articles

Using hybrid element method to solve 3D elliptic crack problems with multi-materials structure

This paper presents a new hybrid element method, based on the finite element alternating technique (FEAT), for calculating the elastic stress-intensity factors for 3D structural components with complex loads, geometry and multiple-materials. It focuses attention on the problem of elliptic cracks. To this end a hybrid element formulation has been developed where the hybrid element has its stiffness matrix corrected to reflect exactly the existence of the true 3D crack geometry within the element. To obtain the stiffness matrix of the hybrid element, this approach involves the combined use of the redundant force method together with the displacement field results arising from the finite element alternating technique. This matrix was subsequently used together with a standard commercial finite element package to obtain the force field of the nodes. Finally these forces were used to determine the stress-intensity factors along the crack front.

A direct traction BIE approach for three-dimensional crack problems

A boundary element (BE) approach based on the traction boundary integral equation for the general solution of three-dimensional (3D) crack problems is presented. The hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular. Regularization and analytical transformation of the boundary integrals is done prior to any boundary discretization. The integration process does not require of any change of coordinates and the resulting integrals can be numerically evaluated in a simple and efficient way. In order to show the generality, simplicity and robustness of the proposed approach, different flat and curved crack problems in infinite and finite domains are analyzed. A simple BE discretization strategy is adopted. The results obtained using rather course meshes are very accurate. The emphasis of this paper is on the effective application of the proposed BE approach and it is pretended to contribute to the transformation of hypersingular boundary element formulation in something as clear, general and easy to handle as the classical formulation but much better suited for fracture mechanics problems.

Comparison of the basic and the discontinuity formulation of the 3D-dual boundary element method

The dual boundary element method (Dual BEM) has established as a numerical approach for solving arbitrary 3D-crack problems in linear elastostatics. In the case of symmetrically loaded cracks — especially traction-free cracks — often the more efficient displacement discontinuity method (DDM) is used, because one obtains a reduced system of algebraic equations. In our paper we will show that the discontinuity method is just a special formulation of the basic Dual BEM and can be applied to arbitrary boundary value problems on the crack. We will present a numerical example for an unsymmetrically loaded crack and discuss which combinations of boundary conditions on the crack surfaces lead to a reduced system of algebraic equations. The savings in memory and computing time compared to the basic formulation of the Dual BEM will be quantified and illustrated by the numerical simulation of 3D crack propagation.

A time-dependent formulation of dual boundary element method for 3D dynamic crack problems

A time-dependent formulation of dual boundary element method for 3D dynamic crack problems

Analysis of 3D crack problems by mapping semi‐analytical BEM

Analysis of 3D crack problems by mapping semi‐analytical BEM

Analysis of 3D crack problems by mapping semi-analytical BEM

By continuous transformation for a domain, this paper develops a new boundary element technique, mapping semi-analytical BEM. Applied to static/dynamic analysis of 3D embedded arbitrarily shaped crack problems, it only needs one-dimensional discretization, so the computational work can be considerably reduced. Some typical examples demonstrate its effectiveness. © 1997 John Wiley & Sons, Ltd.

On the decomposition of the J-integral for 3D crack problems

The extended J-integral for 3D linear elastostatic crack problems and its application to mixed mode problems is investigated. In 3D, the decomposition of the J-integral into its parts corresponding to the symmetric mode I and both antisymmetric modes II and III is derived explicitly. The range of validity of the decomposition method is also discussed in the framework of linear elastic fracture mechanics (LEFM). It is shown analytically that in a general mixed mode case the antisymmetric part of the J-integral can be split into the parts associated with mode II and mode III only in the crack near-field.