ScienceWatch.com (affiliated with Thomson-Reuters), has ranked University of Illinois as the most cited institution in engineering from 1999 to 2009 (http://sciencewatch.com/inter/ins/10/10febTOP20ENG/).  It is followed by Berkeley, MIT, Stanford, University of Michigan, and Georgia Tech.
 
For each institution, ScienceWatch.com has also listed a few research directions that have received most citations.  The mechanics work by Professors Yonggang Huang (University of Illinois), Huajian Gao (Brown University), Bill Nix (Stanford) and Hutchinson (Harvard) on Mechanism-based strain (gradient) plasticity leads the list from the University of Illinois.