Events Calendar

Astani Department of Civil and Environmental Engineering Seminar

Speaker: Dr. Sanjay Govindjee, University of California, Berkeley

Talk Title: Soft and Semi-Soft Elasticity and for Liquid Crystal Elastomers

Abstract: Liquid crystal elastomers present a relatively new and interesting class of materials that display soft and semi-soft elastic behavior as well as viscoelastic behavior. These materials are comprised of liquid crystal molecules together with polymerizing agents to form a final solid that behaves as an elastomeric solid would, as well as like a liquid crystal would. The interaction of these two features provides for a wide and complex range of macroscopically observed phenomena, including for example optical actuation, extreme softness, pattern formation, and high damping to name a few. Because of the wide range of behaviors and the materials highly non-linear properties (material and geometric non-linearities), the modeling of these materials is somewhat challenging. A direct phenomenological approach is generally precluded or only applicable to a small range of loading states. On the other hand, developing models from an atoms-up approach has its own limitations in terms of feasibility. Past efforts mostly involve a compromise and blend of these two approaches, often opaquely, and as such the literature contains a number of different options and viewpoints as to what is important in the modeling of liquid crystal elastomers.
In this presentation, we revisit a number of proposed models for liquid crystal elastomers and try to clearly articulate their meaning. We do this by first examining the fundamental physics associated with the materials constituents. From there we build up, using statistical mechanics arguments, the appropriate structures for describing the materials free-energy functions. This will lead us to an understanding of the meaning of the so-call trace formula for soft elasticity, allowing us to give a precise statement as to what it accounts for and what it does not account for. In particular, we will see that the trace formula is not a strictly entropic result, but rather a hybrid relation. We will also see that the mathematical structure of this energy fails to be quasi-convex and we will discuss the implications of this defect for the solution of boundary value problems with regard to existence of solutions, quasi-convex approximations, and modeling of microstructure evolution. We will next examine microstructural feature of poly-dispersity and see that it gives rise to semi-soft elasticity, and compare and contrast the resulting model structure with a some phenomenological proposals found in the literature for semi-soft elasticity. Time permitting, we will also examine the unique nature of the governing balance laws for these materials which lead to non-symmetric Cauchy stresses.





Biography: Sanjay Govindjee is a Professor of Civil Engineering and the Horace, Dorothy, and Katherine Johnson Endowed Professor at the University of California, Berkeley (1993-2006, 2008-present). His main interests are in theoretical and computational mechanics with an emphasis on micro-mechanics, shape memory alloys, and elastomers. Prior to joining Berkeley he worked as an engineer at the Lawrence Livermore National Laboratory (1991-1993) in Livermore, California. He was also Professor of Mechanics at ETH Zürich (2006-2008) in Zürich, Switzerland.

Sanjay Govindjee obtained a Ph.D. in Mechanical Engineering with a minor in Physics from Stanford University in 1991 under the guidance of the late Prof. Juan C. Simo and a M.S. in Mechanical Engineering from Stanford University in 1987. His S.B. is in Mechanical Engineering from the Massachusetts Institute of Technology in 1986.

Noteworthy honors include a National Science Foundation Career Award, the inaugural 1998 Zienkiewicz Prize and Medal, an Alexander von Humboldt Foundation Fellowship 1999, a Berkeley Chancellor's Professorship 2006-2011, and a guest Professorship at ETH Zürich 2008-2013. In 2015 he was named a Fellow of the US Association for Computational Mechanics. In 2018 he received a Humboldt-Forschungspreis (Humboldt Research Award).

He currently serves as the Principal Investigator and co-Director of the National Science Foundation Natural Hazards Engineering Research Infrastructure SimCenter at Berkeley


Host: Dr. Roger Ghanem

Location: Zoom Meeting https://usc.zoom.us/j/97228056404 Meeting ID: 972 2805 6404 Passcode: 864779

Audiences: Everyone Is Invited

Contact: Evangeline Reyes