Reuleaux plasticity: Analytical backward Euler stress integration and consistent tangent

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 and intermediate principal stress, without incurring the run time penalties of more sophisticated models.