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

Abstract

Additional information: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-prot 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. AbstractThis 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. The key extension provided by this paper is that the yield surface can expand or contract through the movement of control points linked to the level of inelastic straining experienced by the material. The model is integrated using a fully implicit backward Euler algorithm that constrains the return path to the yield surface and allows the derivation of the algorithmic consistent tangent to ensure optimum convergence of the global equilibrium equations. This provides a powerful framework for elasto-plastic constitutive models where, unlike the majority of models presented in the literature, the underlying numerical algorithm (and implemented code) remains unchanged for different yield surfaces. The performance of the algorithm is demonstrated, and validated, using both material point and boundary values simulations including plane stress, plane strain and three-dimensional examples for different yield criteria.

A method for smoothing multiple yield functions

“…Nevertheless, sometimes plastic models are so complicated that it is difficult to formulate a model-specific smoothing procedure. To address this problem, a general strategy has recently been proposed by Coombs et al [26][27][28] These authors use nonuniform rational basis spline (NURBS) surfaces to smooth nondifferentiable yield surfaces. They also describe a stable and efficient implicit stress integration algorithm based on the smooth surface.…”

“…The authors are not aware of another smoothing strategy for this type of plasticity, save for the smoothing proposed in this paper. (In principal, the NURBS approach [26][27][28] could be used, but the choice of control points is not obvious to the authors.) The model is run using unsmoothed multisurface plasticity and the smoothing proposed here with a = 0.02 MPa.…”

On the use of NURBS plasticity for geomaterials

“…The tensile apex of the yield surface poses an issue for the stress return algorithm presented in this paper as the derivatives of the NURBS surface are undefined at this point. Here we follow the same approach as Coombs and Ghaffari Motlagh (2017) and locally round the apex, as shown in Figure 2 with ζ a = 0. Both the original (fine lines) and rounded (thick lines) surfaces are shown in principal stress space.…”

“…Depending on the material analysed the shape of this surface will change and this impacts on the stress integration algorithm 1 (which requires changes in the numerics) for each implemented yield surface. The non-uniform rational basis spline (NURBS) plasticity framework was first proposed by Coombs et al (2016) and extended to include linear isotropic hardening by Coombs and Ghaffari Motlagh (2017). The key idea of the framework is to represent the yield surface of an isotropic plasticity model using a NURBS surface.…”

A Return Mapping Algorithm for Nonlinear Yield Criteria with the Equivalent Mohr–Coulomb Strength Parameters

“…However, these disadvantages are well overcome by constructing return mapping algorithms in the principal stress space [9][10][11][12]. e geometric features of the yield surfaces in the principal stress space can be graphically visualized and are easily and exactly used for determining the return position of updated stress, thereby avoiding the smoothing of nondifferentiable yield surfaces, as other methods involve [12][13][14][15][16][17][18].…”