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

机译：基于屈服函数梯度的数值逼近的简单和计算高效的应力集成方案：应用于高级产量标准

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摘要

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.
机译：在本文中，我们修改了Choi和Yoon提出的压力集成方案[1];基于屈服功能梯度的数值近似，在有限元码中实现，在ABAQUS三种弹性各向同性，塑性各向异性本构模型，屈服于YLD2004-18P [2]，CPB06EX2 [3]和YLD2011-27P [4] ]分别标准。我们已经开发了三个本构模型的Vumat和Umat子程序，并且使用明确的和隐含分析来开发了平面应变张力下的圆柱形杯深绘图测试模拟和动态颈颈部的计算。本文的原始特征是，这些有限元模拟系统地与使用（i）由Choi和Yoon开发的数值近似方案进行的额外计算进行了系统地进行了系统地进行了混合。 （ii）第一和二阶产量函数梯度的分析计算。该比较已经表明，本文提出的屈服功能梯度的数值近似有助于实现本构模型，并且在隐含分析的情况下，它导致计算时间的显着降低而不损害的准确性有限元结果。此外，我们已经证明存在临界加载率，下面有动态隐式分析比显式计算更有效地计算。

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