Comments on a continuum-related Parrinello-Rahman molecular dynamics formulation

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.