  Contractions of Leibniz algebras and Courant algebroids by means of
(1,1)-tensors are introduced and studied. An appropriate version of Nijenhuis
tensors leads to natural deformations of Dirac structures and Lie bialgebroids.
One recovers presymplectic-Nijenhuis structures, Poisson-Nijenhuis structures,
and triangular Lie bialgebroids as particular examples.
