2010 James K. Knowles Lecture
and Caltech Solid Mechanics Symposium


James K. Knowles Lecture

Saturday, February 27, 2010, Beckman Institute Auditorium

The 1st annual James K. Knowles Lecture and Caltech Solid Mechanics Symposium was held on Saturday, February 27, 2010, in the Beckman Institute Auditorium. The inaugural James K. Knowles Lecture by Rohan Abeyaratne,

The Lecture and Symposium are in memory of James K. Knowles, William J. Keenan, Jr. Professor of Applied Mechanics, Emeritus, who passed away on November 1, 2009. He is well known for his research contributions to the theory of nonlinear elasticity and the mathematical theories of materials and structures. Dr. Knowles inspired and influenced generations of students and scholars and authored over one hundred journal publications, as well as a textbook for graduate students entitled Linear Vector Spaces and Cartesian Tensors (Oxford University Press).

The Lecture and Symposium will be held annually and are made possible by the Division of Engineering and Applied Science and the support of family, friends and colleagues through donations to the James K. Knowles Memorial Fund.

"Variations on a Theme by Knowles"

by Rohan Abeyaratne, Berg Professor of Mechanics, Massachusetts Institute of Technology

In a seminal paper* in 1979, Knowles showed that mechanical energy can be dissipated, even in an elastic material, if the motion of the continuum involves a propagating surface of strain discontinuity (such as a shock wave or phase boundary). This opened the door to studying many important questions concerning impact-induced shock waves and the kinetics of phase transitions in solids. Recently, Knowles and I began to investigate the analogous class of problems for a discrete system, i.e., a chain of particles connected by nonlinear springs. There are subtle differences between the continuum and discrete problems. For example, if the discrete system leads to classical nonlinear elasticity theory in the continuum limit, then motions of the continuum might involve strain discontinuities and therefore be dissipative. However the discrete system of particles is conservative. This indicates that the energy balance must behave in a subtle manner as the continuum limit is taken. In this talk I will describe some preliminary work on the dynamics of a one-dimensional chain of particles.

* J.K. Knowles, “On the dissipation associated with equilibrium shocks in finite elasticity,” Journal of Elasticity, 9 (1979), 131-158

Rohan Abeyaratne

Rohan Abeyaratne received his PhD (1979) from the California Institute of Technology working under the guidance of Professor James K. Knowles. Subsequently, Abeyaratne and Knowles engaged in a sustained research collaboration from 1986–2009. Abeyaratne is currently the Berg Professor of Mechanics at MIT and the Director of the Singapore MIT Alliance for Research and Technology (SMART)—a major new research center being established by MIT in Singapore. This, MIT’s first research center outside Massachusetts, is expected to engage over 500 faculty, postdoctoral, and doctoral researchers when it is fully operational. Prior to this, Abeyaratne was Head of the Department of Mechanical Engineering at MIT from 2001–2008 and its Associate Department Head from 1996–2001. Abeyaratne’s field of research interest is theoretical mechanics. A significant part of his work has been focused on the dynamics of phase transitions though he has also done work on homogenization, crack-tip singularities, and cavitation in solids. He co-authored a monograph entitled Evolution of Phase Transitions with Knowles and wrote an ebook entitled Mechanics of Elastic Solids. Volume 1: Mathematical Preliminaries . Abeyaratne is a Fellow of ASME and a Fellow of the American Academy of Mechanics. He has served on the editorial board of four international journals and been on the scientific advisory boards of several universities including the Max Planck Institute for Mathematics in the Sciences and the Aerospace Engineering and Mechanics Department of the University of Minnesota. He recently completed serving a two-year term as President of the American Academy of Mechanics. Abeyaratne holds a MacVicar Fellowship—MIT’s highest award for contributions to education. Despite Knowles’ broad influence on Abeyaratne, which extends to music, nature, politics, fine wines etc., he was continually frustrated by his inability to teach Abeyaratne anything about baseball.

Caltech Solid Mechanics Symposium

Speakers and Topics

Harsha Bhat, Postdoctoral Scholar, Caltech
“Laboratory Earthquakes: A Unique Insight into a Complex Phenomenon”

Chinthaka Mallikarachchi, Graduate Student, Caltech
“CFRP Composite Booms with Integral Tape-Spring Hinges”

Ahmed Ettaf Elbanna, Graduate Student, Caltech
“Pulse-Like Ruptures on Velocity Weakening Frictional Interfaces: Dynamics and Implications”

Hiroyuki Noda, Postdoctoral Scholar, Caltech
“Effects of Shear Heating on Earthquake Dynamics”

Celia Romo, Graduate Student, Caltech
“Multiscale Modeling of Ductile Failure”

Luigi Perotti, Graduate Student, Caltech
“New Finite Element Schemes for Thin Shells”

Phanish Suryanarayana, Graduate Student, Caltech
“Non-Periodic Finite-Element and Mesh-Free Formulation of Kohn-Sham Density Functional Theory”

Justin Brown, Graduate Student, Caltech
“High Pressure Hugoniot Measurements Using Converging Shock Waves in Solids”

Dongchan Jang, Postdoctoral Scholar, Caltech
“Deformation of Materials in Nano Scale: Nanocrystalline and Amorphous Metals”

Alex Spadoni, Postdoctoral Scholar, Caltech
“High Strain-Rate Waves in Granular Media”

Abba Misra, Postdoctoral Scholar, Caltech
“Compressive Behavior of Aligned Carbon Nanotube-Polymer Composites”