Abstract Porous plasticity aims to model the growth and coalescence of voids leading to ductile failure. The GTN model (1984), resulting from heuristic modifications to Gurson's homogenized hollow sphere model (1977), is used in numerous publications. The Rousselier model (1981), developed in the framework of continuum thermodynamics, is apparently similar. Both models are effective in numerical calculations, but the reasons why they perform well were not investigated in details in the existing literature, as regards transition to uniaxial deformation, relations between various modes of strain localization, finite element discretization, regularization. In the present paper, we propose first to revisit both models and to compare their fundamentally different mechanical behaviors. For stress triaxiality larger than some critical value, it is shown that theoretically the GTN model cannot achieve strain localization in a plane but only pointwise localization for the ultimate mechanical state (stress tensor equal to zero). The larger the void volume fraction (void growth), the smaller the stress triaxiality critical value. Fortunately, discretization transforms the pointwise localization into volume localization and with an appropriate Cartesian finite element mesh a more or less planar sheet of integration points can be obtained. The Rousselier model can achieve strain localization in a plane at all stress triaxialities and discretization also transforms this localization into volume localization with a characteristic element size. Second, multiscale modeling of both plasticity and ductile damage (not limited to void damage) is an essential way of progress for laboratory specimen calculations. The Rousselier model can be incorporated into polycrystalline models based on crystal plasticity, with reasonable computation times provided a reduced texture with a small number of crystallographic orientations is used. It can be coupled with a new Coulomb ductile fracture model at the slip system scale and with secondary void nucleation and growth models at the grain and slip system scales, respectively. The multiscale model is applied to aluminum CT and KAHN specimens and to steel round notched specimens.

中文翻译：

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重新审视多孔塑性：宏观和多尺度建模

摘要 多孔塑性旨在模拟导致延性破坏的空隙的增长和合并。GTN 模型 (1984) 源于对 Gurson 均质空心球模型 (1977) 的启发式修改，已在许多出版物中使用。Rousselier 模型 (1981) 在连续热力学的框架内发展起来，显然是相似的。两种模型在数值计算中都是有效的，但现有文献中没有详细研究它们表现良好的原因，如向单轴变形的过渡，各种应变局部化模式之间的关系，有限元离散化，正则化。在本文中，我们建议首先重新审视这两种模型并比较它们根本不同的机械行为。对于大于某个临界值的应力三轴度，结果表明，理论上GTN模型不能实现平面内的应变局部化，而只能实现极限力学状态（应力张量为零）的逐点局部化。空隙体积分数（空隙增长）越大，应力三轴度临界值越小。幸运的是，离散化将逐点定位转换为体积定位，并且通过适当的笛卡尔有限元网格，可以获得或多或少的平面片积分点。Rousselier 模型可以在所有应力三轴下实现平面内的应变局部化，而离散化也将这种局部化转化为具有特征单元尺寸的体积局部化。第二，塑性和延性损伤（不限于空隙损伤）的多尺度建模是实验室试样计算的重要进展方式。Rousselier 模型可以合并到基于晶体塑性的多晶模型中，如果使用具有少量晶体取向的减少纹理，则计算时间合理。它可以分别与滑移系统尺度上的新库仑韧性断裂模型以及晶粒和滑移系统尺度上的二次空隙成核和生长模型相结合。多尺度模型适用于铝 CT 和 KAHN 试样以及钢制圆形缺口试样。使用合理的计算时间提供具有少量晶体取向的减少的纹理。它可以分别与滑移系统尺度上的新库仑韧性断裂模型以及晶粒和滑移系统尺度上的二次空隙成核和生长模型相结合。多尺度模型适用于铝 CT 和 KAHN 试样以及钢制圆形缺口试样。使用合理的计算时间提供具有少量晶体取向的减少的纹理。它可以分别与滑移系统尺度上的新库仑韧性断裂模型以及晶粒和滑移系统尺度上的二次空隙成核和生长模型相结合。多尺度模型适用于铝 CT 和 KAHN 试样以及钢制圆形缺口试样。