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Research

Research Interests

I'm interested in the following research areas:

  • Multiscale Modeling of Materials: A proper understanding of the mechanics and thermodynamics of materials requires a careful analysis of phenomena occurring across a wide span of length and time scales, from the sub-atomic to the continuum, and their scale spanning interactions. A faithful modeling of the material behavior thus necessitates the use of very different models at different scales: quantum mechanics at the sub-atomic scale, classical mechanics at the atomic scale, statistical mechanics at the mesoscale, and effective continuum models at the macro scale. I draw upon tools from mathematics, physics and computation, to explore some of these multiscale aspects of the mechanics and thermodynamics of materials.

  • Wave Propagation in Solids: Mechanical excitations in solids propagate in the form of elastic waves. I'm interested in certain aspects of Structural Health Monitoring, specifically the use of elastic waves to extract information about defects in solids.

Peer-Reviewed Publications

  • M. Ponga, A. A. Ramabathiran, K. Bhattacharya, M. Ortiz. Dynamic behavior of nano-voids in Magnesium under hydrostatic tensile stress. Modelling Simul. Mater. Sci. Eng. 24 065003 (2016).

  • A. A. Ramabathiran, S. Gopalakrishnan. Automatic finite element formulation and assembly of hyperelastic higher order structural models. Applied Mathematical Modelling, Vol. 38, Issues 11--12, Pg. 2867--2883 (2014).

  • S. Gopalakrishnan, A. A. Ramabathiran. Comparative study of different nonconserving time integrators for wave propagation in hyperelastic waveguides. Acta Mech., 225, 2789--2814 (2014).

  • A. A. Ramabathiran, S. Gopalakrishnan. Automatic energy-momentum conserving time integrators for hyperelastic waves. Journal of Computational and Applied Mathematics, Vol. 236, Issue 18, 4700--4711 (2012).

  • A. A. Ramabathiran, S. Gopalakrishnan. Time and frequency domain finite element models for axial waves in hyperelastic rods. Mechanics of Advanced Materials and Structures, Vol. 19, Issue 1--3, 79--99 (2012).

Conferences & Invited Talks

  • A. A. Ramabathiran. A coarse-grained molecular dynamics study of recrystallization of amorphous Silicon. Presented at WCCM XIII, July 22-27, 2018, New York, USA.

  • A. A. Ramabathiran. Coarse-grained atomistic simulation: A quasicontinuum perspective. Talk given at the Indo-Korean workshop organized by IIT Bombay and KIST, January 10-12, 2018, Mumbai, India.

  • A. A. Ramabathiran, M. Ortiz. Mesodynamics: a hybrid deterministic-statistical framework for molecular dynamics. Presented at USNCCM14, July 17-20 2017, Montreal, Canada.

  • A. A. Ramabathiran, A. Pandolfi, M. Ortiz. A new atomistic-to-continuum multiscale framework based on optimal scaling laws for ductile fracture. Presented at Mach Conference 2017, Apr 5-7 2017, Annapolis, USA.

  • A. A. Ramabathiran. Multi-scale modeling and simulation of spall in Magnesium. Invited Talk at University of Colorado, Colorado Springs, Nov. 4, 2016.

  • A. A. Ramabathiran, M. Ortiz. Finite Temperature Quasicontinuum analysis of defects in Magnesium. Poster presented at Dislocations 2016, 19-23 September 2016, Purdue University, West Lafayette, IN, USA.

  • A. A. Ramabathiran, M. Ortiz. Multiscale modeling of twinning and nano-void growth in magnesium. Presented at Mach Conference 2016, 6-8 April 2016, Annapolis, USA.

  • A. A. Ramabathiran, M. Ponga, K. Wang, M. Ortiz. Coarse-grained non-equilibrium atomistic simulation of twinning and void growth in Magnesium. Presented at Mach Conference 2015, 4-7 April 2015, Annapolis, USA.

  • A. A. Ramabathiran, L. Stainier. Staggered schemes for strongly coupled thermoviscoelastic problems based on an energy-based variational formulation of thermomechanics. Presented at XII International Conference on Computational Plasticity (COMPLAS 2013), 3-5 September 2013, Barcelona, Spain.

  • A. A. Ramabathiran, S. Gopalakrishnan. Conserving Integrators for wave propagation in Hyperelastic Layers. Presented at FEMTEC 2011, Third International Conference on Computational Methods in Engineering and Science, South Lake Tahoe, USA.

  • A. A. Ramabathiran, S. Gopalakrishnan. Time and Frequency domain Finite Element analysis of axial wave propagation in weakly nonlinear elastic rods. Presented at Proceedings of ICEAE 2009, IISc, Bangalore, India.

  • A. A. Ramabathiran, S. Gopalakrishnan. Galerkin Finite Element schemes for wave propagation in nonlinear elastic rods. Presented at 50th AIAA SDM conference 2009, Palm Springs, USA.

  • A. A. Ramabathiran, S. Gopalakrishnan. Spectral Finite Element Analysis of wave propagation in Euler-Bernoulli Beams. Presented at ICMMS 2008, IISc, Bangalore, India.

  • A. A. Ramabathiran, K. V. N. Gopal. A finite element based aeroelastic solver for fully geometrically nonlinear rods. Presented at ICMMS 2008, IISc, Bangalore, India.

  • A. A. Ramabathiran, S. Gopalakrishnan, Analysis of wave propagation in 1D rods with first order material nonlinearity using spectral finite element method. Presented at Proceedings of Indo-Russian Workshop on Problems in Nonlinear Mechanics of Solids with Large Deformation, 2006, New Delhi, India.