Abstract
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.
Highlights
This paper offers a compact analytical solution to the backward Euler stress integration for non-associated Reuleaux plasticity
Within energy-mapped stress space, the Non-Associated plastic Flow (NAF) Closest Point Projection (CPP) solution corresponds to that stress state on the yield surface where the normal to the plastic potential passes through the trial stress state
In order to define the consistent tangent for the interface return, we require an equation for the tangent of the intersection arc between the main modified Reuleaux (MR) yield surface and the MR cut-off
Summary
This paper offers a compact analytical solution to the backward Euler stress integration for non-associated Reuleaux plasticity. The paper extends earlier work on (infinitesimal deformation) associated isotropic Reuleaux plasticity [7] by providing, for the first time, closed-form expressions for the Closest Point Projection (CPP) using Energy-Mapped Stress Space (EMSS) [8] for a volumetrically non-associated model incorporating a tension cut-off. Error and runtime analyses for material point simulations are provided, together with finite-element results for (i) the expansion of a thick-walled cylinder, (ii) the expansion of a cylindrical cavity and (iii) the load-deformation behaviour of a rigid strip footing, where associated and non-associated plastic strain contour plots and displacement vectors are compared for infinitesimal and finite deformation simulations. We adopt a tension positive convention and order the principal stresses such that σ1 is the most compressive, while σ3 is the most tensile
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