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Non-associated Reuleaux plasticity : analytical stress integration and consistent tangent for finite deformation mechanics.

Coombs, W.M. and Crouch, R.S. (2011) 'Non-associated Reuleaux plasticity : analytical stress integration and consistent tangent for finite deformation mechanics.', Computer methods in applied mechanics and engineering., 200 (9-12). pp. 1021-1037.


Analytical backward Euler stress integration is presented for a volumetrically non-associated pressure-sensitive yield criterion based on a modified Reuleaux triangle. This advances previous work on associated Reuleaux plasticity using energy-mapped stress space. The analytical solution is 2-4 times faster than a standard numerical backward Euler algorithm. The merit in transforming to (and operating in) this space is that the stress return is truly the closest point on the surface to the elastic trial state. The paper includes a tension cut-off (formed by a second cone) and describes the steps necessary to allow the model's incorporation within a finite deformation framework. Finite-element results show a 59% runtime saving for a modified Reuleaux model over a Willam-Warnke cone giving comparable accuracy in a thick-walled cylinder expansion problem. The consistent tangent provides asymptotically quadratic convergence in the Newton-Raphson scheme under both (i) small strain, infinitesimal deformation and (ii) large strain, finite deformation finite-element simulations. It is shown that the introduction of non-associated flow changes the plastic deformation field and reduces the heave predicted in a plane strain rigid strip-footing problem. The proposed model offers a significant improvement over the Drucker-Prager and Mohr-Coulomb formulations by better reproducing the material dependence on the Lode angle and intermediate principal stress, at little extra computational effort.

Item Type:Article
Keywords:Closest point projection, Computational plasticity, Analytical stress return, Consistent tangent, Finite deformation mechanics, Non-associated plastic flow.
Full text:(AM) Accepted Manuscript
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Publisher statement:This is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 200, 9–12, 2011, 10.1016/j.cma.2010.11.012.
Date accepted:No date available
Date deposited:07 May 2014
Date of first online publication:February 2011
Date first made open access:No date available

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