Ghulam Ishaq Khan Institute of Engineering Science and Technology

A New Class of Multiscale Finite Element Methods:
Application to Fluid and Solid Mechanics

Professor Arif Masud
University of Illinois at Urbana-Champaign

A multiscale finite element framework that is applicable to both structural and fluid systems is presented. This framework allows to embed fine scales of the problem directly into the mathematical formulation. Modeling of the fine scales leads to multiscale-stabilized formulations. The strength of multiscale formulations, especially for multi-physics problems, is highlighted. The limitations of conventional finite element approaches applied to multi-physics problems are outlined.

In fluid dynamics, multiscale method is applied to the incompressible Navier-Stokes equations. The resulting formulation shows superior mathematical and numerical properties that are illustrated via a set of test problems on fluid-structure interactions. In solid mechanics and multiscale material modeling, a two-level scale separation is presented that leads to a mathematically consistent method for bridging molecular mechanics and quasi-continuum mechanics. Contrary to the commonly practiced multigrid/computational nesting of information from smaller scales into the larger ones, a mathematical nesting of scales is proposed via evolution equations for the bridging-scales. Inter-atomic interactions are incorporated through nanoscale based material moduli with internal variables that are functions of the local state of deformation. Point defects are modeled by multi-body inter-atomic potentials. Representative numerical examples are shown to validate the models and demonstrate their range of applicability.

Vita: Professor Arif Masud received Ph.D. in Computational Mechanics from Stanford University in April 1993. He is an Associate Professor of Mechanics and Structures in the Department of Civil and Environmental Engineering (CEE) at the University of Illinois at Urbana-Champaign (UIUC). Before joining UIUC in 2006, Dr. Masud held the appointment of Assistant Professor (1994-2000) and Associate Professor (2000-2006) in the Department of Civil and Materials Engineering (CME), and Department of Bioengineering at the University of Illinois at Chicago (UIC). Dr. Masud is working on the development of multi-scale finite element methods for application in nonlinear solid and fluid mechanics. He has delivered several Keynote Lectures at International Conferences, organized more than ten International Symposia on Multiscale & Stabilized Finite Element Methods, and has served as Guest Editor for five International Journals. He is co-editor of the book The Finite Element Method: 1970s and Beyond that appeared in 2004. In 1999 he was awarded the Teaching Recognition Award by the Council for Excellence in Teaching at UIC, and in 2002 he was awarded the Faculty Distinguished Research Award by the College of Engineering at UIC. Dr. Masud serves on the Editorial Boards of Computer Methods in Applied Mechanics and Engineering, International Journal for Numerical Methods in Fluids, and Journal of Multiscale Computational Engineering. He is Chair of the Computational Mechanics Committee of ASCE, and Vice-Chair of the Fluid Mechanics Committee of ASME. Dr. Masud is an Associate Editor of the ASCE Journal of Engineering Mechanics, and Associate Editor of the ASME Journal of Applied Mechanics. In 2006 he was elected Fellow of the International Association of Computational Mechanics (IACM).