Numerical studies of porous ductile materials containing arbitrary ellipsoidal voids – II: Evolution of the length and orientation of the void axes
Numerical studies of porous ductile materials containing arbitrary ellipsoidal voids – II: Evolution of the length and orientation of the void axes
复制标题
含有任意椭圆体空隙的多孔延性材料的数值研究 - II：空隙轴的长度和方向的演变
DOI：
10.1016/j.euromechsol.2013.06.005
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发表时间：
2013
影响因子：
4.1
通讯作者：
L. Morin
中科院分区：
文献类型：
--
作者：
K. Madou;J. Leblond;L. Morin
在第一部分中，Madou和Leblond，2012 a，Madou和Leblond，2012 b的包含任意椭球形空隙的塑料多孔材料的准则通过将其预测与包含此类空隙的基本单元的一些数值极限分析的结果进行比较来验证。在本第二部分中，我们的目标是通过提出合理的空洞轴的长度和方向的演化方程来完成模型。然而，同样，所提出的方程并不附加到这个特定的模型中，并且可以与任何考虑空隙形状效应的类似标准结合使用。在所寻找的演化方程的定义中，由Ponte-Castaneda和Zaidman（1994）以及Kailasam和Ponte-Castaneda（1998）提出的空洞的应变和旋转速率的“弹性”表达式起着核心作用同质化理论。然而，塑性效应的重要性使得有必要修改这些表达式，这是通过引入应力相关的修正系数来完成的，这些修正系数是在一些参考情况下数值确定的，并在这些情况之间进行适当的插值。
In Part I, Madou and Leblond, 2012a, Madou and Leblond, 2012b's criterion for plastic porous materials containing arbitrary ellipsoidal voids was validated by comparing its predictions with the results of some numerical limit-analyses of elementary cells containing such voids. In the present Part II, our aim is now to complete the model by proposing reasonable evolution equations for the length and orientation of the axes of the voids. Again, however, the equations proposed are not attached to this specific model and could be used in conjunction withanysimilar criterion accounting for void shape effects.In the definition of the evolution equations looked for, a central role is played by “elastic” expressions for the strain and rotation rates of the voids proposed by Ponte-Castaneda and Zaidman (1994) and Kailasam and Ponte-Castaneda (1998) from homogenization theory. The importance of plastic effects however makes it necessary to modify these expressions; this is done heuristically by introducing stress-dependent correction factors determined numerically in a number of reference cases and suitably interpolated between these cases.