The variational principle of safe equilibrium for inhomogeneous elastic cracked bodies is formulated. Using the standard calculus of variations, we show that the crack remains in safe equilibrium as long as the maximum energy reduction rate of the virtually growing crack is negative. The crack starts to grow in the direction of the maximum energy reduction rate when the latter becomes zero. This energetic criterion implies the criteria proposed by He and Hutchinson (1989). As an application we use this criterion to predict the growth direction of an interface crack in a bimaterial.

中文翻译：

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作为变分问题的非均质材料中的安全平衡和裂纹扩展

制定了非均匀弹性裂纹体安全平衡的变分原理。使用标准的变分法，我们表明只要实际增长的裂纹的最大能量减少率为负，裂纹就会保持安全平衡。当后者变为零时，裂纹开始向能量减少率最大的方向发展。这个能量标准暗示了 He 和 Hutchinson (1989) 提出的标准。作为一个应用，我们使用这个标准来预测双材料中界面裂纹的生长方向。