Skip to content

GEOTECH/STRUCT/MAT/CONSTR Seminar: Finite-temperature stress calculation and phonon dispersion evolution in a uniaxially strained anharmonic crystal, Ranganathan Parthasarathy, PhD


Relationships between material structure and mechanical behavior are used to guide the design and improvement of engineering materials. As part of a multi-scale modeling approach, classical molecular dynamics (MD) is frequently used to inform mesoscale models, which are in turn connected to constitutive models at continuum scale. For example, MD has been used to study dislocation mobility and compute finite temperature elastic constants and Peierls stress. However, reconciling continuum stress definitions as work conjugates of strain with stress measures from molecular dynamics simulation is non-trivial, particularly when atomic displacements are non-affine. Even in a homogeneously deforming single crystal, the evolution in thermal fluctuations of atoms is non-affine and contributes significantly to the continuum stress, particularly at high temperatures. For instance, based on neutron scattering experiments and ab initio simulations, vibrational modes have been proposed to be precursors to deformation-induced phase transition or mechanical instability. To quantify the energetic contribution of thermal vibration to the mechanics of deformation, work conjugate stresses have been derived for (a) first order deformation gradients corresponding to atomic equilibrium positions as well as for (b) vibration tensors corresponding to second moments of atomic position. Using MD simulation in NVT ensembles for fcc aluminum subjected to [100] uniaxial extension, the effect of these stress measures on the mechanical behavior in the elastic range and in the vicinity of softening has been demonstrated. Particularly, the experimentally observed phenomenon of reversible vibrational softening is predicted by the derived stress measures at temperatures of 0.7Tm to 0.9 Tm. The phonon dispersion under strained conditions has also been computed using the second moments of atomic position. Anomalies in the phonon dispersion and group velocity distribution are also explained by the non-affine evolution of the thermal lattice vibrations with macroscopic deformation. The results reflect that while the deformation gradient corresponding to equilibrium atomic positions explores the global potential energy well of the system, the vibration tensor explores the local potential wells at individual atomic sites. The results show the usefulness of the derived work-conjugate pairs for multi-scale modeling of high temperature mechanical behavior. The proposed measures are also relevant to polymeric biomaterials such as hydrogels which have a significant entropic contribution to the mechanical behavior.


Dr. Parthasarathy studies mechanical behavior and structure-property relationships of materials. His modeling work involves bridging mechanics from discrete to continuum scale, and is complemented by his experimental work using a range of characterization techniques. He has worked on the following areas:

  • Finite temperature continuum theory based on inter-atomic potentials: Higher order continuum measures from molecular dynamics simulation for crystalline and amorphous solids
  • Soft chemically active fibrous materials: Derivation of poromechanical constitutive laws combining micromechanics of fiber networks and chemical potential of fluid phase for articular cartilage, dentin adhesives, and hydrogels
  • Structure-Property relationships in biomaterials: Developed experimental technique using FTIR imaging and D2O to classify water-polymer interaction from free to bound water. Multi-modal experiments combining mechanical loading and spectroscopic imaging to analyze mechano-sorptive behavior in polymers
  • Multi-physics characterization of biological interfaces: Multivariate statistics applied to hyperspectral data from micro-Raman and FTIR imaging to obtain pseudo-color maps of chemical composition. Coupling of chemical maps with scanning acoustic microscopy to obtain structure property relationships. Method applied to dentin adhesive interface, caries affected dentin, mice kidney, and TMJ disc.
  • Characterization of bonding between super-hard ceramic rhenium diboride with Teflon and high density polyethylene using micro-tensile testing, optical and scanning electron microscopy

Dr. Parthasarathy has co-authored 4 book chapters, 20 peer-reviewed journal publications, and has contributed to 18 presentations of his research results at national and international conferences. He has been a reviewer for 9 journals and is active in professional societies including Engineering Mechanics Institute, Applied Vacuum Society, and European Mechanics society. He chairs minisymposia dealing with computational modeling in the Granular Mechanics group at the Engineering Mechanics Institute Conference.
Teaching Experience
Dr. Parthasarathy currently teaches Engineering Statics, Mechanics of Materials, Structural Testing and Soil Mechanics Laboratory courses at Tennessee State University. He has also taught short courses on Continuum Mechanics and Finite Element Method as part of NNSA-MSIPP Computational Modeling Workshops, General Physics including Mechanics and Thermodynamics, and assisted with teaching applied courses on Biomaterials, Computer Simulation in Biomechanics, and Biofluids.

Thursday, November 29, 2018 at 3:40pm to 5:00pm

John D. Tickle Engineering Building, 405
851 Neyland Dr, Knoxville, TN 37996

Event Type

Lectures & Presentations




Current Students, Faculty & Staff, General Public


CEE Seminar, CEE Fall 2018


Civil and Environmental Engineering

Google Calendar iCal Outlook

Recent Activity