- 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.
- Nonlinear elasticity and anelasticity
- Geometric mechanics
- Computational mechanics
- Mechanics of bulk and surface growth
- Engineering Fracture Mechanics Top 10 Most Cited Articles, 2005 to 2009.
- ScienceDirect Top25 Hottest Articles (see publications)
- 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
- 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
- Bill Schultz Junior Faculty Teaching Award, Georgia Institute of Technology, 2007
- A. Angoshtari and A. Yavari, Hilbert complexes of nonlinear elasticity. Zeitschrift fur Angewandte Mathematik und Physik (ZAMP), DOI: 10.1007/s00033-016-0735-y.
- S. Sadik and A. Yavari, Small-on-large geometric anelasticity. Proceedings of the Royal Society A, to appear.
- A. Angoshtari, M.F. Shojaei, and A. Yavari, Compatible-strain mixed finite element methods for 2D nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering, DOI: 10.1016/j.cma.2016.09.047.
- F. Sozio and A. Yavari, Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies, Journal of the Mechanics and Physics of Solids 98, 2017, pp. 12-48.
- A. Yavari, A. Ozakin, and S. Sadik, Nonlinear elasticity in a deforming ambient space, Journal of Nonlinear Science 26(6), pp. 1651-1692.
- A. Yavari and A. Goriely (2015). 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)
- 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.
- 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, 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.
- Nonlinear Mechanics of Surface Growth for Cylindrical and Spherical Elastic Bodies, Society of Engineering Science (SES) 53th Annual Technical Meeting, University of Maryland, College Park, October 3, 2016.
- Compatible-Strain Mixed Finite Elements for 2D Compressible Nonlinear Elasticity, The 12th World Congress on Computational Mechanics, Seoul, South Korea, July 26, 2016.
- Nonlinear Elasticity in a Deforming Ambient Space, The Role of Mechanics in the Study of Lipid Bilayers, International Center for Mechanical Sciences (CISM), Udine, Italy, July 14, 2016.
- Discombinations in Nonlinear Elastic Solids, Emerging Trends in Applied Mathematics and Mechanics, Perpignan, France, May 31, 2016.
- Finite Dilatational, Torsional, and Shear Eigenstrains in Nonlinear Elastic Solids. Universitat Politecnica de Catalunya Barcelonatech, Spain, May 27, 2016.