  We consider the shape-topological control of a singularly perturbed
variational inequality. The geometry-dependent state problem that we address in
this paper concerns a heterogeneous medium with a micro-object (defect) and a
macro-object (crack) modeled in 2d.
  The corresponding nonlinear optimization problem subject to inequality
constraints at the crack is considered within a general variational framework.
For the reason of asymptotic analysis, singular perturbation theory is applied
resulting in the topological sensitivity of an objective function representing
the release rate of the strain energy. In the vicinity of the nonlinear crack,
the anti-plane strain energy release rate is expressed by means of the mode-III
stress intensity factor, that is examined with respect to small defects like
micro-cracks, holes, and inclusions of varying stiffness. The result of
shape-topological control is useful either for arrests or rise of crack growth.
