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Abstract: Atomistic simulation has been a powerful study tool in mechanics research,but how to objectively compute the atomic stress equivalent to Cauchy stress isstill controversial, especially on the velocity-related part in the virialstress definition. In this paper, by strictly following the classicaldefinition of the Cauchy stress for continuum medium, the fundamentalLagrangian atomic stress is proposed and can be used to obtain the correctCauchy stress under any circumstances. Furthermore, the Lagrangian virialstress is proposed, which is still in virial form but does not includevelocities to avoid controversial velocity treatments. It is also found thatthe widely used classical virial stress is actually the Eulerian virial stress,which includes the velocities of atoms, and is valid only when theimpulse-momentum theorem is applicable to estimate the internal forces. Howeverthis requirement for the Eulerian atomic stress can not always be met inpractical cases, such as the material volume element in rotation and theexamples presented in this paper, but the proposed Lagrangian atomic stress canavoid these velocity-related nonobjectivities.

Author: B. Liu, X. Qiu



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