The non-uniqueness of the atomistic stress tensor and its relationship to the generalized Beltrami representation

Nikhil Chandra Admal, Ellad B Tadmor

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

The non-uniqueness of the atomistic stress tensor is a well-known issue when defining continuum fields for atomistic systems. In this paper, we study the non-uniqueness of the atomistic stress tensor stemming from the non-uniqueness of the potential energy representation. In particular, we show using rigidity theory that the distribution associated with the potential part of the atomistic stress tensor can be decomposed into an irrotational part that is independent of the potential energy representation, and a traction-free solenoidal part. Therefore, we have identified for the atomistic stress tensor a discrete analog of the continuum generalized Beltrami representation (a version of the vector Helmholtz decomposition for symmetric tensors). We demonstrate the validity of these analogies using a numerical test. A program for performing the decomposition of the atomistic stress tensor called MDStressLab is available online at http://mdstresslab.org.

Original languageEnglish (US)
Pages (from-to)72-92
Number of pages21
JournalJournal of the Mechanics and Physics of Solids
Volume93
DOIs
StatePublished - Aug 1 2016

Keywords

  • Atomistics
  • Constitutive behavior
  • Residual stress
  • Stress concentration
  • Stress relaxation

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