The Boundary Integral Equation (BIE) method has occupied me to
various degrees for the past twenty-two years. The attraction of
BIE analysis has been its unique combination of mathematics and
practical application. The EIE method is unforgiving in its
requirement for mathe matical care and its requirement for
diligence in creating effective numerical algorithms. The EIE
method has the ability to provide critical inSight into the
mathematics that underlie one of the most powerful and useful
modeling approximations ever devised--elasticity. The method has
even revealed important new insights into the nature of crack tip
plastic strain distributions. I believe that EIE modeling of
physical problems is one of the remaining opportunities for
challenging and fruitful research by those willing to apply sound
mathematical discipline coupled with phys ical insight and a desire
to relate the two in new ways. The monograph that follows is the
summation of many of the successes of that twenty-two years,
supported by the ideas and synergisms that come from working with
individuals who share a common interest in engineering mathematics
and their application. The focus of the monograph is on the
application of EIE modeling to one of the most important of the
solid mechanics disciplines--fracture mechanics. The monograph is
not a trea tise on fracture mechanics, as there are many others who
are far more qualified than I to expound on that topic."
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