Extreme Structures in Composites

Abstract

In theory of composites or micro-structures, it is important to find inclusion shapes with special property. In relation to such shapes, Eshelby showed that an ellipsoidal shape, which produces the minimal energy, has internal uniform strains for any given uniform loading and then conjectured that ellipsoids are the only shape (structure) with such a uniformity property. The speaker will present some recent results on this Eshelby’s conjecture. He and his collaborators also consider a coated structure called neutral inclusion, the insertion of which does not perturb the given outside uniform field. Hashine showed that some confocal ellipsoids are neutral inclusions and used them to construct a composite having a given effective property. The speaker will investigate the question whether confocal ellipsoids are the only structure of such. Some positive answers will be presented.

About the speaker

Prof. Hyundae Lee received his BS, MS and PhD, all in Mathematics, from Seoul National University in 1998, 2002 and 2006 respectively. He undertook postdoctoral research at Seoul National University in 2006-2007 and at École Polytechnique in 2007-2008. He joined Inha University in 2008 and is currently an Associate Professor at the Department of Mathematics.

Prof. Lee's research focuses on composite materials including metamaterials and inverse problems related to medical imaging. He was awarded the Sangsan Prize for Young Mathematicians by the Korean Mathematical Society in 2009.

About the program

For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.