A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

The cohesive zone model: advantages, limitations and challenges

The comprehensive body of knowledge that has built up with respect to the friction stir welding (FSW) of aluminium alloys since the technique was invented in 1991 is reviewed The basic principles of FSW are described, including thermal history and metal flow, before discussing how process parameters affect the weld microstructure and the likelihood of entraining defects After introducing the characteristic macroscopic features, the microstructural development and related distribution of hardness are reviewed in some detail for the two classes of wrought aluminium alloy (non-heat-treatable and heat-treatable) Finally, the range of mechanical properties that can be achieved is discussed, including consideration of residual stress, fracture, fatigue and corrosion It is demonstrated that FSW of aluminium is becoming an increasingly mature technology with numerous commercial applications In spite of this, much remains to be learned about the process and opportunities for further research a

Friction stir welding of aluminium alloys

Lectures on Cauchy’s Problem in Linear Partial Differential Equations. By J. Hadamard. Pp. viii+316. 15s.net. 1923. (Per Oxford University Press.)

Publisher Summary This chapter discusses some basic problems in mechanics of elastic solids containing multiple cracks. A number of mathematical aspects that frequently constitute fields of their own (like various numerical techniques) are discussed very briefly in the chapter. The focus is on physically important effects produced by crack interactions and to present results in the simplest form possible. The problems considered in this chapter can be divided into two groups: (1) The impact of interactions on individual cracks, particularly on the stress intensity factors (SIFs), and (2) the effective elastic properties of solids with many cracks. Problems of the first group are, generally, relevant for the fracture-related considerations; solutions are sensitive to the positions of individual cracks. Problems of the second group deal with the volume average quantities; they are relatively insensitive to the information on individual cracks. The chapter discusses, in this connection, whether correlations exist between these two groups of quantities; in particular, whether microcracking can be reliably monitored by measuring changes in the effective elastic moduli.

Elastic Solids with Many Cracks and Related Problems

SUMMARY The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite-part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack-edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J-integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed-mode conditions.

https://msvlab.hre.ntou.edu.tw/cite/DualBEM_Crack_Aliabadi_IJNME_1992.pdf

The dual boundary element method: Effective implementation for crack problems

This text bridges the gap between existing specialist books on theoretical fracture mechanics, and texts on numerical methods. It concentrates on the application of the boundary element method to fracture mechanics, although an account of recent advances in other numerical methods is presented.

Numerical Fracture Mechanics

Boundary Element Formulations in Fracture Mechanics

In this paper, an effective numerical implementation of the three-dimensional dual boundary element method, for linear elastic crack problems, is presented. Displacement and traction integral equations which constitute the dual boundary formulation are used independently on crack surfaces to overcome the numerical difficulties associated with co-planar crack surfaces in boundary element analysis. The crack surfaces are modelled with discontinous quadrilateral quadratic elements. The use of discontinous elements allow for accurate integration of finite part integrals. The accuracy of the proposed method is demonstrated by solving a number of problems including edge and embedded cracks.

M.H. Aliabadi

Papers

The dual boundary element method: Effective implementation for crack problems

Numerical Fracture Mechanics

Boundary Element Formulations in Fracture Mechanics

Dual boundary element method for three-dimensional fracture mechanics analysis

Dual boundary element incremental analysis of crack propagation