Mechanics and Computation / View source

for Unified Interface Formulations combining Discontinuous Galerkin and Variational Multiscale Methods
=Arif Masud, Ph.D.=

===December 1, 2011===

Unified Interface Formulations combining 
Discontinuous Galerkin and Variational Multiscale Methods

This talk presents concepts from discontinuous Galerkin (DG) methods to derive a generalized variational formulation for modeling interfacial phenomena in solid mechanics. Specifically, the displacement continuity and traction equilibrium conditions along the interface are enforced in a weak sense via jump terms evaluated in integral expressions along the interface. We proceed through the highlights of this derivation for the case of isotropic mixed elasticity in conjunction with stabilization emanating from Variational Multiscale (VMS) concepts, resulting in a finite element method that accommodates a wide range of material and problem classes. The formulation is subsequently specialized to two important applications: multi-faceted domain problems on nonmatching meshes and contact mechanics problems involving Coulomb friction. A major attribute of integrating the Continuous- and Discontinuous-Galerkin methods via the VMS framework is that the resulting methods come equipped with a built-in error estimation feature that produces feedback on the level of discretization error in the computed solution. Furthermore, the DG jump terms provide a mechanism for embedding constitutive laws for material response at the interface in a variationally consistent fashion.
The second part of the talk presents extension of the stabilized mixed formulation for large deformation hyperelasticity derived using the Variational Multiscale ideas with a focus on linear simplex/simplicial elements. The method is applied to simulate materials governed by a spectrum of isotropic and anisotropic constitutive models in the finite strain range to illustrate its versatility. Additionally, the classical F-bar method is encompassed by the present formulation through specific choices of the multiscale models. Finally, we show that the fine-scale error estimates developed for small strain elasticity trivially carry over to the finite deformation context.

Vita: Arif Masud received Ph.D. in Computational Mechanics from Stanford University in April 1993. He is a Professor of Engineering Mechanics in the Department of Civil and Environmental Engineering at the University of Illinois at Urbana-Champaign. He holds joint appointments in the Department of Aerospace Engineering, Computational Science and Engineering, and the Center for Micro-&-Nanotechnology. Dr. Masud has made fundamental contributions to the development of Multiscale and Stabilized finite element methods for nonlinear fluid and solid mechanics. He has authored or co-authored over 100 refereed journal articles, conference papers, and book chapters on these topics, and is co-editor of the book Finite Element Method: 1970’s and Beyond.  He is past Chair of the Fluid Mechanics Committee of ASME, past Chair of the Computational Mechanics Committee of ASCE, and served as the General Conference Chair for the ASME Applied Mechanics and Materials Conference held in Chicago in May 2011. Dr. Masud serves as an Associate Editor of the ASCE Journal of Engineering Mechanics, Associate Editor of the ASME Journal of Applied Mechanics, and Associate Editor of ASCE Journal of Nanomecahnics and Micromechanics. He was elected a Fellow of the International Association of Computational Mechanics (IACM) in 2006, Fellow of the American Society of Mechanical Engineers (ASME) in 2008, and Fellow of the U.S. Association of Computational Mechanics (USACM) in 2009. In 2010 he was named Robert H. Dodds Faculty Scholar in the Department of Civil Engineering, University of Illinois.
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