A simple and computationally efficient stress integration scheme based on numerical approximation of the yield function gradients: Application to advanced yield criteria Articles uri icon

publication date

  • September 2021

start page

  • 1

end page

  • 21


  • 103538


  • 192

International Standard Serial Number (ISSN)

  • 0168-874X

Electronic International Standard Serial Number (EISSN)

  • 1872-6925


  • In this paper, we have modified the stress integration scheme proposed by Choi and Yoon [1]; which is based on the numerical approximation of the yield function gradients, to implement in the finite element code ABAQUS three elastic isotropic, plastic anisotropic constitutive models with yielding described by Yld2004-18p [2], CPB06ex2 [3] and Yld2011-27p [4] criteria, respectively. We have developed both VUMAT and UMAT subroutines for the three constitutive models, and have carried out cylindrical cup deep drawing test simulations and calculations of dynamic necking localization under plane strain tension, using explicit and implicit analyses. An original feature of this paper is that these finite element simulations are systematically compared with additional calculations performed using (i) the numerical approximation scheme developed by Choi and Yoon [1]; and (ii) the analytical computation of the first and second order yield functions gradients. This comparison has shown that the numerical approximation of the yield function gradients proposed in this paper facilitates the implementation of the constitutive models, and in the case of the implicit analyses, it leads to a significant decrease of the computational time without impairing the accuracy of the finite element results. In addition, we have demonstrated that there is a critical loading rate below which the dynamic implicit analyses are computationally more efficient than the explicit calculations.


  • Mechanical Engineering


  • advanced yield criteria; anisotropy; stress integration; finite elements; metal forming