Title : 
Microscopic mechanism of strain localisation in amorphous materials 

Speaker  :  Ratul Dasgupta, Weizmann Institute of Science, Israel 
Date  :  July 12, 2013 
Time  :  12:00 PM 
Venue  :  CARE seminar room 
Abstract  : 
A large class of amorphous or disordered materials ranging from "hard" bulkmetallic glasses to "soft" foams, exhibit strain localisation when subject to a sufficiently large deformation. This particular phenomenon often leads to material failure and thus obtaining a microscopic understanding of this process becomes very important. In recent work, we have studied the instability responsible for this process from a microscopic point of view using athermal, quasistatic simulations of binary LennardJones glasses and continuum solid mechanics. The talk will start with an introduction to some of the basic ideas in amorphous elasticity & plasticity. The importance of nonaffine motion, the notion of elementary plastic instabilities in the stressstrain response and the connection between nonaffine response and eigenvalues & eigenmodes of the Hessian matrix will be discussed brief?y. Data obtained from numerical simulations show that the nonaffine displacement field associated with a plastic instability undergoes a qualitative shift, changing from a quadrupolar field to a shear band as we strain the material. We will understand this transition using the theoretical formalism of Eshelby inclusion(s). An expression for the elastic energy of N inclusions dispersed and oriented randomly in an elastic medium subject to a global loading will be obtained. It will then be proven analytically that at sufficiently large values of strain, a state of minimal energy is when each of these N inclusions are equialigned and lie on a line oriented at 45° to the global compressive axes. It will be seen that this highly correlated arrangement of inclusions, is responsible for organising the nonaffine flow into a shear band. A formula for yieldstrain obtained from this calculation, will be presented. Extension of these ideas to account for finite temperature and ﬁnite strainrates will also be discussed. In a second and shorter part of the talk, I will also present some of my Ph.D. work on laminar, hydraulic jumps and the connection to nonlinear waves. Results from freesurface NavierStokes simulations of hydraulic jumps in both planar and circular geometries will be discussed and some interesting theoretical analysis will be presented in brief. 