The Mechanics and Mathematics of Bodies Described by Implicit Constitutive Equations: Specific Applications

Plenary Lecture, 14th Pan-American Congress of Applied Mechanics

K. R. Rajagopal

Distinguished Professor, Regents Professor, Forsyth Chair in Mechanical Engineering, Professor of Mathematics, Professor of Biomedical Engineering, Professor of Civil Engineering, Professor of Chemical Engineering, Senior Research Scientist, Texas Transportation Institute

Department of Mechanical Engineering, Room 314, Engineering Physics Building, College Station, TX 77843-3 123, U.S.A.

University of Texas A&M


I will discuss specific applications wherein implicit response relations can be gainfully exploited. It will be shown that such implicit relations can explain phenomena that have hitherto defied adequate explanation such as fracture and the movement of cracks in solids, and such models can describe the response of fluids and solids with properties that depend both on the invariants of the stress and appropriate kinematical variables. The models also provide a new way to look at turbulence in fluids.  Implicit models also provide a framework for describing important problems concerning the flow of non-linear fluids through porous media due to high pressure gradients. Moreover, such implicit constitutive relations lead to governing equations that possess characteristics which are desirable both from the point of view of qualitative mathematical and numerical analysis.

BIO: Professor Rajagopal holds a B. Tech. from the Indian Institute of Technology, Madras (1973), a M.S. from the Illinois Institute of Technology (1974), and a Ph.D. from the University of Minnesota, where his PhD advisor was Roger Fosdick. At the present K. R. Rajagopal is a Distinguished Professor at the Department of Mechanical Engineering of the University of Texas, where he also holds appointments in other departments such as the Department of Mathematics, and the Department of Civil Engineering. His research interests focus on Continuum Mechanics and its applications to Non-linear materials. Among his different honours and distinctions we can mention the Eringen Medal, which he received from the Society of Engineering Science in 2004 and the Bush Excellence Award received also in 2004. Professor Rajagopal has been editor and has been in the editorial board of many journals, such as the Archive for Rational Mechanics and Analysis, the International Journal of Engineering Science, the International Journal of Nonlinear Mechanics, Meccanica, Journal of Elasticity, Continuum Mechanics and Thermodynamics, International Journal of Plasticity, and Theoretical and Computational Fluid Mechanics.

Organized by: 14th Pan-American Congress of Applied Mechanics
When: Monday, March 26th, 2014 at 8:30 AM
Where: Hotel Nippon. Barón Pierre de Coubertin 62, Santiago, Chile