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Numerical implementation and assessment of a phenomenological nonlocal model of ductile rupture

机译：塑性破裂现象学非局部模型的数值实现与评估

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Just like all constitutive models involving softening, Gurson's [A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part Ⅰ - Yield criteria and flow rules for porous ductile media, ASME J. Engrg. Mater. Technol. 99 (1977) 2-15] model of ductile rupture predicts unlimited localization of strain and damage. Leblond et al.'s [J.B. Leblond, G. Perrin, J. Devaux, Bifurcation effects in ductile metals with nonlocal damage, ASME J. Appl. Mech. 61 (1994) 236-242] have proposed to solve this problem in a heuristic way by using a nonlocal evolution equation for the porosity, which expresses its time-derivative as a spatial convolution integral of some "local porosity rate". This paper is devoted to the numerical implementation and assessment of this phenomenological variant of Gurson's model. The numerical implementation proposed bears some resemblance to Aravas's [N. Aravas, On the numerical integration of a class of pressure-dependent plasticity models, Int. J. Numer. Methods Engrg. 24 (1987) 1395-1416] classical one but departs from it through use of an explicit algorithm with respect to the porosity, if not with respect to other parameters. The main reason for this choice lies in the proof of existence and uniqueness, for such an algorithm, of the solution of the "projection problem" onto Gurson's yield locus. The assessment of the model is based on two criteria, absence of mesh size effects in finite element computations and agreement of experimental and numerical results for some typical ductile fracture tests. Since the first topic has already been investigated by Tverg-aard and Needleman's [V. Tvergaard, A. Needleman, Effects of nonlocal damage in porous plastic solids, Int. J. Solids Struct. 32 (1995) 1063-1077], we concentrate on the second one. Unfortunately, numerical experience reveals that the modification of Gurson's model envisaged degrades the agreement between experimental results and model predictions. A theoretical analysis of this phenomenon is presented. Although based on crude simplifying assumptions, this analysis suffices to qualitatively explain the failure of the model and suggest a simple remedy. Numerical experience confirms that this remedy considerably improves numerical predictions. Thus, with this modification, Leblond et al. (1994)'s proposal appears as a viable solution to the problem of unlimited localization of strain and damage in Gurson (1997)'s model.
机译：就像所有涉及软化的本构模型一样，Gurson [A.L. Gurson，通过空洞形核和生长产生的延性破裂的连续理论：第一部分-多孔延性介质的屈服准则和流动规则，ASME J.工程。母校技术。 99（1977）2-15]韧性断裂模型预测应变和损伤的无限局限性。 Leblond等人的著作[J.B. Leblond，G。Perrin，J。Devaux，具有非局部损伤的易延展金属中的分叉效应，ASME J. Appl。机甲[J.Am.Chem.Soc.61（1994）236-242]提出了通过对孔隙度使用非局部演化方程来以启发式的方式解决该问题，该方程将其时间导数表示为某些“局部孔隙率”的空间卷积积分。本文致力于Gurson模型这一现象学变体的数值实现和评估。提出的数字实现与Aravas的[N. Aravas，关于一类压力相关可塑性模型的数值积分，国际。 J.纽默方法工程。 [J.Am.Chem.Soc.24（1987）1395-1416]的经典方法，但是如果不考虑其他参数，则通过使用关于孔隙率的显式算法而偏离它。这种选择的主要原因在于，对于这种算法，证明了“投影问题”在Gurson屈服轨迹上的存在性和唯一性。该模型的评估基于两个标准，即有限元计算中不存在网格尺寸影响，以及某些典型延性断裂试验的实验和数值结果一致。由于第一个主题已经由特维尔-阿德（Tverg-aard）和尼德曼（Needleman）的著作[V. Tvergaard，A。Needleman，多孔塑料固体中非局部损伤的影响，国际。 J.固体结构。 32（1995）1063-1077]，我们专注于第二个。不幸的是，数值经验表明，所设想的Gurson模型的修改降低了实验结果与模型预测之间的一致性。对该现象进行了理论分析。尽管基于粗略的简化假设，但此分析足以定性地解释模型的失败并提出一种简单的补救措施。数值经验证实，该补救措施可大大改善数值预测。因此，通过这种修改，Leblond等人。 （1994）的建议似乎是对Gurson（1997）模型中应变和损伤的无限局部化问题的可行解决方案。

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