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Comments on a Continuum-Related Parrinello-Rahman Molecular Dynamics Formulation

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Abstract

Phase transitions in solid mechanics are commonly studied employing Parrinello-Rahman molecular dynamics. This type of molecular dynamics may lead to a proper description of the atomistic scale in multi-scale analysis of engineering problems. However, the proposed Lagrangian is stated without derivation and lacks invariance under modular transformations. Recently, this type of dynamics was re-interpreted into a continuum-related Parrinello-Rahman molecular dynamics. The continuum-related formulation is derived in a consistent physical manner and becomes equal to the original formulation by employing two propositions. The propositions are stated without validation and the treatment shows no numerical example demonstrating the performance of the proposed formulation. Based on this recent continuum-related derivation, this paper investigates the validity of the two propositions in a numerical example, namely a phase transition in a nickel single crystal. Furthermore, the invariance of the continuum-related Lagrangian is investigated. This implies that the obtained dynamics is invariant to the chosen unit cell, which corroborates with results in solid state physics and which is a mandatory requirement for the suitability for multi-scale analysis.

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Acknowledgements

The author would like to express his sincere gratitude to Houfu Fan, University of California at Berkeley, for his help in the numerical implementation. Furthermore, the author would like to thank Prof. Antonio DiCarlo, Roma Tre University, for an enlightening and pleasant short-term stay with his group in Rome and Prof. Paolo Podio-Guidugli for establishing the contact and arranging the stay. The instructive comments made by the reviewers are thankfully acknowledged.

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  1. Institute for Strength of Materials, Graz University of Technology, Kopernikusgasse 24/I, 8010, Graz, Austria

    Manfred H. Ulz

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  1. Manfred H. Ulz
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Correspondence to Manfred H. Ulz.

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Ulz, M.H. Comments on a Continuum-Related Parrinello-Rahman Molecular Dynamics Formulation. J Elast 113, 93–112 (2013). https://doi.org/10.1007/s10659-012-9412-3

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  • DOI: https://doi.org/10.1007/s10659-012-9412-3

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