Stability of the numerical procedure for solution of singular integral equations on semiinfinite interval  Application to fracture mechanics
Abstract
Singular integral equations (Cauchytype singularity) play a key role in computational fracture mechanics. In modeling the micromechanical aspects of fracture, effects produced by defects with dimensions much smaller than the crack size are examined. Thus, to focus attention on these effects, a crack has to be considered as infinitely large and the problem has to be brought to a defect scale. The integral equations resulting from these problems are formulated on a semiinfinite interval, and they are of the first kind with Cauchytype singular term. On a finite interval, the numeric procedure for these equations is well developed and analyzed. On a semiinfinite interval, this procedure cannot be directly applied without a stabilization of the numerical scheme. The existence of a solution to a homogeneous equation creates a stability problem in forming the numerical scheme. Depending on the mesh size, different magnitudes of the homogeneous solutions can be sensed by the numerical scheme. A numerical procedure with a stabilizing term and its implementations in fracture mechanics on microscale is discussed.
 Publication:

Computers and Structures
 Pub Date:
 July 1992
 Bibcode:
 1992CoStr..44...71R
 Keywords:

 Cauchy Integral Formula;
 Crack Geometry;
 Fracture Mechanics;
 Numerical Stability;
 Singular Integral Equations;
 Stress Intensity Factors;
 Computer Techniques;
 Crack Propagation;
 Crack Tips;
 Micromechanics;
 Structural Mechanics