The problem of identification of the load applied to a membrane from
measurements of its displacement is considered. A partially breaking
of the structure (depending on the gradient of the displacement) is modelled
by a non-smooth constitutive law. A geometrical variable --- the set of all points,
where the critical value for breaking is exceeded --- and the problem is
reformulated as a shape optimization problem for the geometric variable.
Shape sensitivity analysis and the level-set method are used for the numerical
solution of the problem.