Volume 116, Number 3, November 2016
|Number of page(s)||7|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||21 December 2016|
The origin of the distinction between microscopic formulas for stress and Cauchy stress
Department of Mechanical and Aerospace Engineering, University of Florida - Gainesville, 32611, FL, USA
Received: 25 May 2016
Accepted: 28 November 2016
Stress is calculated routinely in atomistic simulations. The widely used microscopic stress formulas derived from classical or quantum mechanics, however, are distinct from the concept of Cauchy stress, i.e., the true mechanical stress. This work examines various atomistic formulations for local stress and their inconsistencies. Using standard mathematic theorems and the law of mechanics, we show that Cauchy stress results unambiguously from the definition of internal force density, thereby removing the long-standing confusion about the atomistic basis of the fundamental property of Cauchy stress and leading to a new atomistic formula for local stress The new atomistic stress formula has clear physical meaning and well-defined values, satisfies the conservation law, and is fully consistent with the concept of Cauchy stress.
PACS: 45.20.-d – Formalisms in classical mechanics / 05.20.-y – Classical statistical mechanics / 02.70.Ns – Molecular dynamics and particle methods
© EPLA, 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.