The Mechanics and Mathematics of Bodies Described by Implicit Constitutive Equations: General Considerations

The Mechanics and Mathematics of Bodies Described by Implicit Constitutive Equations: General Considerations

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  • March 20, 2014
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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

In successful classical theories such as linearized elasticity or the Navier-Stokes theory one finds an explicit relationship for the stress in terms of the appropriate kinematical quantity. The same is true of Cauchy elasticity and the Rivlin-Ericksen model for fluids. However, there are many natural phenomena that cannot be adequately described by such explicit constitutive representation and one needs implicit theories wherein one has a true relation between the stress and its various time derivatives and appropriate kinematical quantities and their time derivative. Motivation will be provided for the need for implicit response relations to describe the behavior of both non-linear fluids and solids, especially with a view of the possibility of their use to describe and understand phenomena that have hitherto been inadequately and incorrectly described. I will list several applications wherein they can be gainfully exploited.

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 25th, 2014 at 8:30 AM
Where: Hotel Nippon. Barón Pierre de Coubertin 62, Santiago, Chile

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