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

Coombs, W.M. & 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. doi: 10.1016/j.cma.2010.11.012


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.

Publication Type: Article
Additional Information: © 2011, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Publisher Keywords: Closest point projection; Computational plasticity; Analytical stress return; Consistent tangent; Finite deformation mechanics; Non-associated plastic flow
Subjects: T Technology > TJ Mechanical engineering and machinery
Departments: School of Science & Technology > Engineering
Text - Accepted Version
Available under License : See the attached licence file.

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