Geometric frustration and the intrinsic approach in materials science

19 Sep
Widely Applied Mathematics Seminar
Dr. Efi Efrati
Thursday, September 19, 2019 - 3:00pm to 4:00pm
Pierce 209

Geometric frustration arises whenever a structure is endowed with two or more mutually contradicting geometric tendencies. Such systems do not possess a stress-free rest state and thus are best described through intrinsic geometric quantities such as their metric. While the metric description of incompatible elasticity, which describes frustrated solids, is relatively developed and has seen much use in recent years, applications of these ideas outside of the field of solid mechanics are scarce.

In this talk, I will discuss how the concepts of geometric frustration and accurate intrinsic description allow new understandings when applied to liquid crystals and to analyze viscoelastic instabilities.

For 2D liquid crystals, the local bend and splay take the role played by the Riemannian metric in solids. We show that exploiting these intrinsic variables allows us not only to properly account for geometric frustration in liquid crystals but also to solve the general inverse design problem of nematic elastomers: finding the director field which will yield a desired metric upon a uniform biaxial deformation.

For viscoelastic solids, the intrinsic description leads to a reformulation of the theory in terms of a temporally evolving reference metric. This allows us to analytically address the notion of stability in viscoelastic structures, predict the future stability of viscoelastic systems and formulate guiding principles for their behavior. We conclude by demonstrating the quantitative agreement with experiments in viscoelastic shells displaying delayed viscoelastic buckling.    

Speaker Bio: 

Dr. Efrati received his undergraduate and PhD from Hebrew University where he studied math and physics under the guidance of Eran Sharon and Raz Kupferman.

He was a Simons postdoctoral fellow at the James Frank Institute in the University of Chicago.

In 2014 he joined the Department of Physics of Complex systems in the Weizmann Institute of Science. 

Prof. Amir