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

Abstract

In this paper, we have modified the stress integration scheme proposed by Choi and Yoon (2019), 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 (Barlat et al., 2005), CPB06ex2 (Plunkett et al., 2008 and Yld2011-27p (Aretz and Barlat, 2013) 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 (2019), 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.

The effect of material orientation on void growth

“…Moreover, the elastic-plastic constitutive model presented in Section 2 has been implemented in ABAQUS/Standard (2016) through a UMAT subroutine, using the integration algorithm based on numerical approximation of the yield function gradients developed by Hosseini and Rodríguez-Martínez (2021).…”

“…both CPB06ex2 and Yld2011-27p yield criteria in ABAQUS/Standard (2016) through a UMAT subroutine using the integration scheme reported in Hosseini and Rodríguez-Martínez (2021). In the finite element calculations we use the material parameters reported by Plunkett et al (2008) and Aretz and Barlat (2013).…”

The effect of voids shape on hypervelocity cylindrical cavity expansion and shock waves formation in transversely isotropic porous materials

“…All the theoretical results presented in this work have been compared with finite element simulations performed in Abaqus/Explicit using a VUMAT subroutine, in which the model of Monchiet et al (2008) was implemented following the integration scheme developed by Hosseini and Rodríguez-Martínez (2021). The agreement between numerical simulations and theoretical model predictions for all the cavitation velocities and material features investigated in this work provides additional verification of the cavity expansion solution, supporting the results and conclusions presented in this paper (the comparison is not shown for the sake of brevity).…”

Theoretical predictions of dynamic necking formability of ductile metallic sheets with evolving plastic anisotropy and tension-compression asymmetry

“…The finite element model is meshed with eight-node solid elements, with reduced integration and hourglass control (C3D8R in ABAQUS notation), with dimensions ≈ 25 × 25 × 50 μm 3 (elements are initially shorter along the loading directions). The constitutive model presented in Section "Constitutive framework" has been implemented in ABAQUS/Standard [2] and ABAQUS/ Explicit [1] via UMAT and VUMAT user subroutines, respectively, using the stress-update algorithm based on the numerical approximation of the yield function gradients developed by Hosseini and Rodríguez-Martínez [25]. The UMAT [2] has been used to obtain the low strain rate finite element results, 0.0001 s − 1 and 100 s − 1 , reported in Figs.…”