NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

Abstract

. (2016) 'NURBS plasticity : yield surface representation and implicit stress integration for isotropic inelasticity.', Computer methods in applied mechanics and engineering., 304 . pp. 342-358. Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn numerical analysis the failure of engineering materials is controlled through specifying yield envelopes (or surfaces) that bound the allowable stress in the material. However, each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case. These equations impact on the numerical implementation, specifically relating to stress integration, of the models and therefore a separate algorithm must be constructed for each model. This paper presents, for the first time, a way to construct yield surfaces using techniques from non-uniform rational basis spline (NURBS) surfaces, such that any isotropic convex yield envelope can be represented within the same framework. These surfaces are combined with an implicit backward-Euler-type stress integration algorithm to provide a flexible numerical framework for computational plasticity. The algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration. The performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models.

NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening

“…Consistent with the work of Coombs et al [8], most of the paper is presented in terms of principal stresses with a tension positive notation and the conventional ordering…”

“…Typically the form of the yield surface impacts on the stress integration algorithm which requires changes in the numerics for each implemented yield surface. This issue was overcome by the paper of Coombs et al [8] for yield surfaces that are fixed in stress space, known as perfect plasticity. It allowed any smooth isotropic yield surface to be modelled without changing the numerical algorithm or underlying code by using non-uniform rational basis spline (NURBS) surfaces to represent the yield envelope.…”

“…This paper extends the non-uniform rational basis spline (NURBS) plasticity framework of Coombs et al [8] to include isotropic hardening of the yield surfaces. The approach allows any smooth isotropic yield envelope to be represented by a NURBS surface.…”

“…Here we follow the approach of Coombs et al [8] and adopt an implicit stress integration algorithm (elastic prediction followed by a plastic correction) coupled with an associated flow plasticity formulation that expresses the yield envelope as a NURBS surface. This allows any smooth isotropic yield function to be included within the same numerical framework.…”

Cyclic Plastic Hinges with Degradation Effects for Frame Structures

“…A NURBS-based approach was suggested in (Coombs et al 2016), that can in principle accurately approximate any yield surface, provided the control points can be chosen appropriately. Hardening may be introduced via movement of the control points, providing an option of modifying the shape of the yield surface locally during hardening.…”