Faculty Profile

BIOGRAPHY

  • Ph.D. (Mechanical Engineering, Applied Mechanics Option with Minor in Mathematics), California Institute of Technology, 2005
  • M.S. (Mechanical Engineering), The George Washington University, 2000
  • B.S. (Civil Engineering), Sharif University of Technology, Tehran, Iran, 1997

Professor Yavari joined the School of Civil and Environmental Engineering at the Georgia Institute of Technology in January 2005. He received his B.S. in Civil Engineering from Sharif University of Technology, Tehran, Iran in 1997. He continued his studies at The George Washington University where he obtained an M.S. in Mechanical Engineering in 2000. He then moved to Pasadena, CA and obtained his Ph.D. in Mechanical Engineering (Applied Mechanics option with minor in Mathematics) from the California Institute of Technology in 2005. Professor Yavari is a member of the American Academy of Mechanics.
Professor Yavari's interests are in developing systematic theories of discrete mechanics for crystalline solids with defects. Defects play a crucial role in determining the properties of materials. The development of atomistic methods including density functional theory, bond-order potentials and embedded atom potentials has enabled a detailed study of such defects. However, much of the work is numerical and often with ad hoc boundary/far-field conditions. Specifically, a systematic method for studying these discrete yet non-local problems is lacking. Design in small scales requires solving inverse problems and this is not possible with purely numerical techniques. From a mechanics point of view, defective crystals are modeled as discrete boundary-value problems. The challenging issues are extending the existing techniques from solid state physics for non-periodic systems, new developments in the theory of vector-valued partial difference equations, existence and uniqueness of solutions of discrete boundary-value problems and their symmetries, etc. The other efforts in this direction are understanding the geometric structure of discrete mechanics and its link with similar attempts in the physics and computational mechanics literatures and investigating the rigorous continuum limits of defective crystals.
It has been known in physics for quite some time that the configuration spaces of physical phenomena, in general, are not linear, i.e. Euclidean, and instead they are manifolds (finite or infinite dimensional). Modeling physical theories on manifolds has been pursued for several decades in the theoretical physics literature and ideas from differential geometry have led to many profound advances in physics, the most celebrated one being Einstein's general theory of relativity. In engineering, and in particular in mechanics, manifold theory has not been appreciated perhaps mainly because engineering scientists have been involved in solving many specific technological problems in the last few decades and this has forced them to work with the simplest possible mathematical models.  This need of working with simple models formulated in Euclidean spaces has resulted in a disconnect between different methods and a lack of deep understanding of the connections between different numerical methods, structure of governing equations of discrete and continuous systems, etc.  One of Dr. Yavari's interests is to use ideas and techniques from differential geometry, exterior calculus, and algebraic topology in several problems in continuum and discrete mechanics in order to advance the understanding of different aspects of mechanics of continuous and discrete systems and their connections, differences and similarities.

RESEARCH INTERESTS

  • Geometric continuum mechanics
  • Mechanics of defects
  • Nonlinear elasticity
  • Solid mechanics in small scales
  • Ferroelectrics
  • Fracture mechanics.

HONORS & AWARDS

  • US Junior Oberwolfach Fellow, 2013
  • OCCAM Visiting Fellow, Mathematical Institute, University of Oxford, Summer 2013
  • Mathematics and Mechanics of Solids, Editorial Board Member 2011
  • OCCAM Visiting Fellow, Mathematical Institute, University of Oxford, Summer 2011
  • Engineering Fracture Mechanics Top 10 Most Cited Articles, 2005 to 2009.
  • AFOSR Young Investigator Program Award, 2010
  • OCCAM Visiting Fellow, Mathematical Institute, University of Oxford, Summer 2010
  • Excellence in Research Award, Georgia Institute of Technology, 2010
  • ScienceDirect Top25 Hottest Articles (see publications)
  • Bill Schultz Junior Faculty Teaching Award, Georgia Institute of Technology, 2007

RECENT PUBLICATIONS & PRESENTATIONS

ARTICLES
  • A. Yavari and A. Goriely, The geometry of discombinations and its applications to semi-inverse problems in anelasticity, Proceedings of the Royal Society A 470, 2014, 20140403.
  • R. Mirzaeifar, T. Zhu, K. Gall, A. Yavari, and R. DesRoches. Structural transformations in NiTi shape memory alloy nanowires, Journal of Applied Physics 115, 2014, 194307.
  • A. Ozakin and A. Yavari, Affine development of closed curves in Weitzenbock manifolds and the Burgers vector of dislocation mechanics, Mathematics and Mechanics of Solids 19, 2014, pp. 299-307.
  • N.D. Afify, H.G. Salem, A. Yavari, and T. El Sayed, Consolidation of nanometer-sized aluminum single crystals: microstructure and defects evolutions, Computational Materials Science 85, 2014, pp. 306-309.
  • A. Yavari and A. Goriely, Riemann-Cartan geometry of nonlinear disclination mechanics, Mathematics and Mechanics of Solids 18(1), 2013, pp. 91-102.
BOOKS
  • A. Yavari and A. Goriely (2014). Non-Metricity and the Nonlinear Mechanics of Distributed Point Defects. In: R. J. Knops, G.-Q. Chen, and M. Grinfeld (Editors), Differential Geometry and Continuum Mechanics, Springer Proceedings in Mathematics & Statistics (PROMS).
  • Yavari, A. and M.P. Wnuk (2009). Finite Fracture Mechanics for Fractal Cracks. In: F. M. Borodich (Editor) IUTAM Symposium on Scaling in Solid Mechanics, Springer, pp. 223-231.
  • A. Yavari and A. Angoshtari (2013). Atomic Structure of 180^o Ferroelectric Domain Walls in PbTiO_3. In: S. Li and X-L. Gao (Editors), Handbook of Micromechanics and Nanomechanics, Pan Stanford Publishing.
PROCEEDINGS
  • A. Yavari, Nonlinear Mechanics of Point Defects and Weyl Geometry. 10th World Congress on Computational Mechanics. July 8-13. Sao Paulo, Brazil.
  • R. Mirzaeifar, R. DesRoches, A. Yavari . K. Gall. Bending analysis of textured polycrystalline shape memory alloy beams. ASME Conference on Smart Materials, Adaptive Structures & Intelligent Systems (SMASIS 2012). September 19-21. Stone Mountain, Georgia, USA.
  • A. Yavari. Riemann-Cartan Geometry of Nonlinear Dislocation Mechanics, 12th Pan American Congress of Applied Mechanics. January 2-6, 2012. Port of Spain, Trinidad.
  • A. Yavari. Discrete Fracture Mechanics of Rough Cracks, 12th Pan American Congress of Applied Mechanics. January 2-6, 2012. Port of Spain, Trinidad.
  • R. Mirzaeifar, R. DesRoches, A. Yavari . K. Gall. A Closed-form Solution for Superelastic Shape Memory Alloy Beams Subjected to Bending. SPIE Smart Structures/NDE (2012). March 11-15. San Diego, California, USA.
PRESENTATIONS
  • A. Yavari, Nonlinear Elastic Inclusions in Nonlinear Isotropic Solids. Fakultat fur Mathematik, Universitat Duisburg-Essen, Germany, September 5, 2014.
  • A. Yavari, Differential Complexes in Continuum Mechanics, IUTAM Symposium on innovative numerical approaches for materials and structures in multi-feld and multi-scale problems, Burg Schnellenberg, Germany, September 2, 2014.
  • A. Yavari, Non-Riemannian Geometries and the Nonlinear Mechanics of Distributed Defects, RIMS International Conference: Mathematical Challenge to a New Phase of Materials Science, Kyoto University, Japan, August 4-9, 2014.
  • A. Yavari, Non-Riemannian Geometries and the Nonlinear Mechanics of Distributed Defects, Multiscale Materials Modeling: Mathematical and Computational Aspects, 7th US -- France Symposium, Rensselaer Polytechnic Institute, June 10-11, 2014.
  • A. Yavari, Nonlinear Elastic Inclusions in Nonlinear Isotropic Solids. Fourteenth Pan American Congress of Applied Mechanics, Santiago, Chile, March 24, 2014.