AEROSPACE ENGINEERING

Abstract

The Peierls-Nabarro (PN) model is a classic example of a continuum model of the core structure of dislocations that removes the well-known singularity associated with the linear elastic model of dislocations. In conjunction with the generalized stacking fault energy functional proposed by Vitek, the PN model can be systematically refined using data from atomistic scale simulations such as molecular statics or density functional theory. The first half of this talk will focus on a new and recently developed numerical scheme to solve the PN model based on the inverse Hilbert transform. The primary advantage of this numerical scheme is that it reduces the solution of the nonlinear and nonlocal PN model to a simple fixed-point iteration scheme. The proposed scheme will be illustrated by using it to resolve the core structure of edge and screw dislocations on close-packed {111} slip planes in face-centered cubic materials. The second part of the talk will focus on recent and ongoing work on the use of certain machine learning techniques to develop atomistically accurate nonlocal extensions of the PN model. The larger goal of this study is to gain insight into the use of modern machine learning algorithms to develop constitutive models of material behavior. A more immediate goal, in the context of dislocation core structures, is to revisit the assumptions and limitations inherent in the use of the generalized stacking fault energy to model the misfit energy associated with the slip plane in the PN model. A nonlocal misfit energy functional is proposed in this regard as a correction to the generalized stacking fault energy. Kernel ridge and Gaussian process regression are employed to train both the generalized stacking fault energy and the nonlocal misfit energy function using data from molecular statics simulations. The utility of this machine-learned nonlocal model in resolving dislocation core structures will then be discussed by investigating certain representative edge and screw dislocation cores in fcc and bcc materials. Finally, some of the implications of this nonlocal model on the collective behavior of dislocations will be briefly discussed in the context of phase field dislocation dynamics models.

Speaker

Dr. Amuthan Ramabathiran

Assistant Professor in the Department of Aerospace Engineering at Indian Institute of Technology (IIT) Bombay. His primary research interests include the development of theoretical and computational tools for multiscale modeling in the context of crystalline and amorphous materials, wave propagation in elastic solids, and machine learning in the context of computational mechanics. He received his Ph.D. (2012) in Aerospace Engineering from the Indian Institute of Science and B.Tech (2005) and M.Tech (2006) (dual) degrees in Aerospace Engineering from IIT Madras. Prior to joining IIT Bombay, he was a postdoctoral researcher at Caltech and Ecole Centrale de Nantes (France).