Implementation of isotension ensemble in molecular dynamics

The implementation of the new type of ensemble, with constant tension force in the molecular dynamic simulations, is considered. In contrast to the isostress NtT ensemble, in which the stress components act on the surface and the volume elements, the new NfT ensemble is determined by the tension forces acting on each particle in the extended space. Correspondingly, instead of the stress-strain relation used in conventional theory, a new type of constitutive equation in terms of stretch and tension becomes an objective of the molecular dynamics simulations. Comparison with the Parrinello-Rahman method is made for the general external load and the temperature applied. Results for the aluminum lattice show that the suggested approach gives an unbiased sampling of the isostress-isothermal ensemble in the LAMMPS environment. Additionally, the problem of atomistic boundary condition was renovated, due to almost identical tension and traction forces. It was shown on several examples of strains that the tension forces properly represent the type and magnitude of the atomistic external load applied to the surface, despite the absence of any quantities related to the area in the constitutive equations. An analog of Cauchy's stress theorem in the new setting is formulated and verified by numerical simulations.