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ERROR ESTIMATORS FOR VISCOPLASTIC MATERIALS: APPLICATION TO FORMING PROCESSES

机译：粘弹塑性材料的误差估算器：在成形过程中的应用

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摘要

The analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non-linear materials. Firstly, Zienkiewicz-Zhu (Z~2) type error estimators are studied. They are based on the comparison between the finite element solution and a continuous solution which is computed by smoothing technique. From numerical examples, it is shown that the choice of a finite difference smoothing method (Orkisz' method) improves the precision and the efficiency of this type of estimator. Then a Δ estimator is introduced. It makes it possible to take into account the fact that the smoothed solution does not verify the balance equations. On the other hand, it leads us to introduce estimators for the velocity error according to the L~2 and L~∞ norms, since in metal forming this error is as important as the energy error. These estimators are applied to an industrial problem of extrusion, demonstrating all the potential of the adaptive remeshing method for forming processes.
机译：误差估计的分析是在粘塑性问题（即不可压缩和非线性材料）的框架内解决的。首先，研究Zienenewewicz-Zhu（Z〜2）型误差估计器。它们基于有限元解与通过平滑技术计算的连续解之间的比较。从数值示例中可以看出，选择有限差分平滑方法（Orkisz方法）可以提高此类估计器的精度和效率。然后引入Δ估计器。可以考虑以下事实：平滑解决方案无法验证平衡方程。另一方面，它导致我们根据L〜2和L〜∞范数引入速度误差的估计量，因为在金属中，此误差与能量误差同等重要。这些估算器应用于挤出的工业问题，证明了自适应再成形方法在成形过程中的所有潜力。

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