Woodruff School of Mechanical Engineering

Faculty Candidate Seminar


An anisotropic non-singular theory of dislocations with atomic resolution


Dr. Giacomo Po


Mechanical and Aerospace Engineering Department, University of California


Monday, April 11, 2016 at 11:00:00 AM


MRDC Building, Room 4211


Chaitanya Deo


The singular nature of the elastic fields produced by dislocations presents conceptual chal-lenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in a particular version of Mindlin’s anisotropic gradient elasticity with up to six independent gradient parameters. The framework models anisotropic materials where there are two sources of anisotropy, namely the bulk material ani-sotropy and a weak non-local anisotropy relevant at the nano-scale. The Green tensor of this framework, which we derive as part of the work, is non-singular and it rapidly converges to its classical counterpart a few characteristic lengths away from the origin. Therefore, the new Green tensor can be used as a physical regularization of the classical Green tensor. The Green tensor is the basis for deriving a non-singular eigenstrain theory of defects in anisotropic mate-rials, where the non-singular theory of dislocations is obtained as a special case. The funda-mental equations of curved dislocation loops in three dimensions are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line inte-gral form of the generalized solid angle associated with dislocations having a spread core. The six characteristic length scale parameters of the framework are obtained from the components of the rank-six tensor of strain gradient coefficients of Mindlin’s theory. In turn, the compo-nents of such tensor are obtained from atomistic calculations. As an extension of the Born-Huang lattice theory of elasticity, we show that the rank-six tensor of strain gradient coeffi-cients admits an explicit local representation in terms of the derivatives of atomistic potentials. By virtue of this explicit representation, the link between atomistic and the simplified theory of gradient elasticity is established, and a non-singular and parameter-free theory of disloca-tions in anisotropic materials is obtained. Several applications of the theory are presented.


Giacomo Po is a Postdoctoral Fellow and Lecturer in the Mechanical and Aerospace Engineer-ing Department at the University of California Los Angeles (UCLA). He received his Ph.D. in Mechanical Engineering from UCLA in 2011. His research interest focuses on the mechanics of materials defects in metals and ceramics, with emphasis on discrete and continuum models of dislocation-based plasticity. Giacomo is the main developer of the Mechanics of Defects Evolution Library (MoDEL), an open-source and multi-physics framework for the Discrete Dislocation Dynamics method. His work has been published in several scientific journals, in-cluding the Journal of the Mechanics and Physics of Solids, Acta Materialia, Physical Review, The Journal of Nuclear Materials, Physical Letters, the Journal of Applied Physics, and others.


Refreshments will be served.