On the use of Reuleaux plasticity for geometric non-linear analysis

Coombs, W. M.; Crouch, R. S.; Augarde, C. E.

Abstract

Three dimensional analyses including geometric and material non--linearity require robust, efficient constitutive models able to simulate engineering materials. However, many existing constitutive models have not gained widespread use due to their computational burden and lack of guidance on choosing appropriate material constants. Here we offer a simple cone-type elasto-plastic formulation with a new deviatoric yielding criterion based on a modified Reuleaux triangle. The perfect plasticity model may be thought of as a hybrid between Drucker-Prager (D-P) and Mohr-Coulomb (M-C) that provides control over the internal friction angle independent of the shape of the deviatoric section. This surface allows an analytical backward Euler stress integration on the curved surface and exact integration in the regions where singularities appear. The attraction of the proposed algorithm is the improved fit to deviatoric yielding and the one--step integration scheme, plus a fully defined consistent tangent. The constitutive model is implemented within a lean 3D geometrically non-linear finite-element program. By using an updated Lagrangian logarithmic strain--Kirchhoff stress implementation, existing infinitesimal constitutive models can be incorporated without modification.

Citation

Coombs, W. M., Crouch, R. S., & Augarde, C. E. (2010, April). On the use of Reuleaux plasticity for geometric non-linear analysis. Presented at 18th UK Conference on Computational Mechanics (ACME), Southampton, England

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 18th UK Conference on Computational Mechanics (ACME)
• Start Date: Apr 8, 2010
• End Date: Apr 10, 2010
• Publication Date: Mar 1, 2010
• Deposit Date: Sep 13, 2011
• Publicly Available Date: Apr 14, 2016
• Pages: 113-116
• Keywords: Closest point projection, Analytical stress return, Energy mapped stress space, Consistent tangent, Finite deformation mechanics
• Public URL: https://durham-repository.worktribe.com/output/1158439
• Publisher URL: http://www.acmeuk.org/