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

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