  The use of the interaction integral to compute stress intensity factors
around a crack tip requires selecting an auxiliary field and a material
variation field. We formulate a family of these fields accounting for the
curvilinear nature of cracks that, in conjunction with a discrete formulation
of the interaction integral, yield optimally convergent stress intensity
factors. We formulate three pairs of auxiliary and material variation fields
chosen to yield a simple expression of the interaction integral for different
classes of problems. The formulation accounts for crack face tractions and body
forces. Distinct features of the fields are their ease of construction and
implementation. The resulting stress intensity factors are observed converging
at a rate that doubles the one of the stress field. We provide a sketch of the
theoretical justification for the observed convergence rates, and discuss
issues such as quadratures and domain approximations needed to attain such
convergent behavior. Through two representative examples, a circular arc crack
and a loaded power function crack, we illustrate the convergence rates of the
computed stress intensity factors. The numerical results also show the
independence of the method on the size of the domain of integration.
