Finite-temperature stress calculations in atomic models using moments of position

Journal of Physics. Condensed Matter : an Institute of Physics Journal
Ranganathan ParthasarathyLizhi Ouyang

Abstract

Continuum modeling of finite temperature mechanical behavior of atomic systems requires refined description of atomic motions. In this paper, we identify additional kinematical quantities that are relevant for a more accurate continuum description as the system is subjected to step-wise loading. The presented formalism avoids the necessity for atomic trajectory mapping with deformation, provides the definitions of the kinematic variables and their conjugates in real space, and simplifies local work conjugacy. The total work done on an atom under deformation is decomposed into the work corresponding to changing its equilibrium position and work corresponding to changing its second moment about equilibrium position. Correspondingly, we define two kinematic variables: a deformation gradient tensor and a vibration tensor, and derive their stress conjugates, termed here as static and vibration stresses, respectively. The proposed approach is validated using MD simulation in NVT ensembles for fcc aluminum subjected to uniaxial extension. The observed evolution of second moments in the MD simulation with macroscopic deformation is not directly related to the transformation of atomic trajectories through the deformation gradient using ...Continue Reading

References

Oct 4, 2003·Physical Review Letters·D M ClatterbuckJ W Morris
May 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Saswati GangulyMadan Rao
Mar 11, 2015·Zeitschrift für angewandte Mathematik und Mechanik·Anil MisraPaulette Spencer

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Citations

Dec 19, 2018·Biointerphases·Ranganathan ParthasarathyPaulette Spencer

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