Equations are developed to describe the evolution of internal parameters entering the formulation of any criterion of unhomogeneous yielding. The evolution equations are applicable to arbitrarily oriented ellipsoidal voids. The parameters include the volume fraction of voids, the relative lengths and orientations of their axes, and their relative spacings. The evolution equations are determined in terms of the average strain-rate and rotation-rate for the voids, which are assumed to remain ellipsoidal. The point of departure consists of expressions available in the literature for incompressible elastic solids. Complementary fields are then introduced to satisfy the strong kinematic constraints of unhomogeneous yielding. The relations capture the lateral void enlargement under tension, which is key to predicting void coalescence through internal necking, as well as void shearing, which is essential to the formation of flat elliptical micro-cracks. The evolution equations are evaluated against numerical limit analysis results, and correction factors are introduced for improved quantitative predictions.

中文翻译：

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多孔材料的不均匀屈服 — 演化方程


开发方程来描述进入任何非齐次屈服准则的公式的内部参数的演变。演化方程适用于任意方向的椭球空隙。这些参数包括空隙的体积分数、空心轴的相对长度和方向以及空心的相对间距。演化方程是根据空隙的平均应变速率和旋转速率确定的，假设它们保持椭球体。出发点包括文献中可用的不可压缩弹性固体的表达式。然后引入互补场以满足非均匀屈服的强运动学约束。这些关系捕捉了受拉作用下的横向空隙扩大，这是通过内部颈缩预测空隙聚结的关键，也是空隙剪切的关键，这对于形成平坦的椭圆形微裂纹至关重要。根据数值极限分析结果对演化方程进行评估，并引入校正因子以改进定量预测。