The geometric and distributive properties of voids significantly influence anisotropic coalescence behaviour. However, this problem has received little attention owing to the complexity of considering all the properties in the current analytical framework of limit analysis. To address this issue, this study proposes an analytical framework based on an elliptic coordinate system, including the determination of the ligament zone, characterization of plastic flow, and derivation of the void coalescence criterion, for porous materials with various geometric and distributive properties, including size, shape, spacing, and orientation. This framework is motivated by our observations that the evolution of the void geometry and surrounding plastic flow can be well characterized by the grid of the elliptic coordinate system. Subsequently, an analytical function is proposed to determine the ligament zone and coalescence direction with various void properties. A hollow nonaxisymmetric cylindrical unit cell is proposed to describe this ligament zone, and the corresponding trial velocity field is derived by extending the previous Gurson-like velocity field into the elliptic cylindrical coordinate system. The rationality of the field is validated by comparing its equivalent strain rate field with numerical simulations. Finally, a coalescence criterion is derived via the limit analysis of the proposed unit cell undergoing internal necking. Two heuristic adjustments are formulated for the overflow phenomenon in the rigid zone and outer ligament zones. Numerical assessments with various void properties confirm the accuracy of the analytical model. The coalescence criterion can predict the independent and coupling effects of geometric and distributive properties on anisotropic void coalescence. This study provides possible solutions to future plasticity problems of ellipsoidal inclusions.

中文翻译：

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考虑几何和分布特性的椭圆柱空隙各向异性合并


空隙的几何和分布特性显着影响各向异性聚结行为。然而，由于在当前极限分析的分析框架中考虑所有属性的复杂性，这个问题很少受到关注。为了解决这个问题，本研究提出了一个基于椭圆坐标系的分析框架，包括韧带区的确定、塑性流动的表征以及空隙合并准则的推导，适用于具有各种几何和分布特性的多孔材料，包括尺寸、形状、间距和方向。该框架的灵感来自于我们的观察，即椭圆坐标系的网格可以很好地表征空隙几何形状和周围塑性流动的演变。随后，提出了一种分析函数来确定具有各种空隙特性的韧带区域和合并方向。提出用中空的非轴对称圆柱晶胞来描述该韧带区域，并通过将先前的类古尔森速度场扩展到椭圆圆柱坐标系中来导出相应的试验速度场。通过等效应变率场与数值模拟的比较，验证了该场的合理性。最后，通过对所提出的经历内部颈缩的晶胞的极限分析得出聚结标准。针对刚性区和外韧带区的溢出现象制定了两种启发式调整。对各种空隙特性的数值评估证实了分析模型的准确性。 合并准则可以预测几何和分布特性对各向异性空洞合并的独立和耦合影响。这项研究为未来椭圆体包裹体的塑性问题提供了可能的解决方案。