Molecular dynamics at constant Cauchy stress

Ronald E. Miller, Ellad B. Tadmor, Joshua S. Gibson, Noam Bernstein, Fabio Pavia

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7 Scopus citations


The Parrinello-Rahman algorithm for imposing a general state of stress in periodic molecular dynamics simulations is widely used in the literature and has been implemented in many readily available molecular dynamics codes. However, what is often overlooked is that this algorithm controls the second Piola-Kirchhoff stress as opposed to the true (Cauchy) stress. This can lead to misinterpretation of simulation results because (1) the true stress that is imposed during the simulation depends on the deformation of the periodic cell, (2) the true stress is potentially very different from the imposed second Piola-Kirchhoff stress, and (3) the true stress can vary significantly during the simulation even if the imposed second Piola-Kirchhoff is constant. We propose a simple modification to the algorithm that allows the true Cauchy stress to be controlled directly. We then demonstrate the efficacy of the new algorithm with the example of martensitic phase transformations under applied stress.

Original languageEnglish (US)
Article number184107
JournalJournal of Chemical Physics
Issue number18
StatePublished - May 14 2016

Bibliographical note

Funding Information:
R.M. and J.G. gratefully acknowledge funding from NSERCs discovery and Accelerator programs. E.T. was partly supported through the National Science Foundation (NSF) under Grant No. CMMI-1433887. N.B.s work was supported by ONR through NRLs basic research program. Simulations were performed on the computational resources at

Publisher Copyright:
© 2016 Author(s).

Copyright 2018 Elsevier B.V., All rights reserved.

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