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School of Engineering and Computing Sciences (ECS)

Profile

Publication details for Dr Charles Augarde

Coombs, W.M., Crouch, R.S. & Augarde, C.E. (2010). Reuleaux plasticity: analytical backward Euler stress integration and consistent tangent. Computer Methods in Applied Mechanics and Engineering 199(25-28): 1733-1743.
  • Publication type: Journal papers: academic
  • ISSN/ISBN: 0045-7825
  • DOI: 10.1016/j.cma.2010.01.017
  • Keywords: Closest point projection, Computational plasticity, Analytical stress return, Energy-mapped stress space, Consistent tangent.
  • View online: Online version
  • Durham research online: DRO record

Author(s) from Durham

Abstract

Analytical backward Euler stress integration is presented for a deviatoric yielding criterion based on a
modified Reuleaux triangle. The criterion is applied to a cone model which allows control over the shape of
the deviatoric section, independent of the internal friction angle on the compression meridian. The return
strategy and consistent tangent are fully defined for all three regions of principal stress space in which elastic
trial states may lie. Errors associated with the integration scheme are reported. These are shown to be less
than 3% for the case examined. Run time analysis reveals a 2.5–5.0 times speed-up (at a material point) over
the iterative Newton–Raphson backward Euler stress return scheme. Two finite-element analyses are
presented demonstrating the speed benefits of adopting this new formulation in larger boundary value
problems. The simple modified Reuleaux surface provides an advance over Mohr–Coulomb and Drucker–
Prager yield envelopes in that it incorporates dependencies on both the Lode angle