A Unified Interpretation of Stress in Molecular Systems

Central-force decomposition of spline-based modified embedded atom method potential

“…This is a natural, and, as shown by Admal and Tadmor [53], the most justifiable decomposition, because it provides a stress tensor which is symmetric and which also satisfies the balance of linear and angular momentum. While all pair potentials satisfy both (1) and (2), it is not immediately obvious whether the above conditions, and (2) in particular, are satisfied in the case of more involved potentials, particularly for many-body potentials.…”

“…Murdoch [44] introduced spatial and temporal averaging to the IK procedure, which was another way of circumventing the use of Dirac delta distributions and obviated the need to calculate ensemble averages. The approach of [43,44] (termed the Murdoch-Hardy procedure, with the corresponding quantity known as Hardy stress) was later further generalised [45][46][47][48][49][50][51][52][53][54]. Owing to its many advantages, Hardy stress has since found widespread use in atomistic simulations [55][56][57][58][59][60][61][62][63][64].…”

“…Other approaches to the calculation of local stress have been proposed over time [36-38, 40, 65], with the definition itself often an object of debate [40,48,50,51,[53][54][55]. The features of a number of measures of local stress were examined in detail by Admal and Tadmor [53,54], who showed through numerical experiments [53] that of the three most commonly used approaches, Hardy stress is the most accurate approach, with the most favourable convergence with respect to the averaging volume.…”

“…The features of a number of measures of local stress were examined in detail by Admal and Tadmor [53,54], who showed through numerical experiments [53] that of the three most commonly used approaches, Hardy stress is the most accurate approach, with the most favourable convergence with respect to the averaging volume.…”

“…In [53] it was shown that for any multi-body potential with a continuously differentiable extension, the force that acts on a particle can always be expressed as a sum of central forces. In this work, building on the observations of Admal and Tadmor [53], we present expressions for the central force decomposition for potentials of the s-MEAM class [11], the popularity of which we expect to rise significantly in the near future.…”