We consider the n-component transversely isotropic unidirectional elastic composites, the longitudinal axis of which is parallel to those of the transversely isotropic components as well as the generators of the cylindrical phase boundaries between them. From the minimum energy and complementary energy principles, with appropriate constant strain and piece-wise constant stress trial fields, optimization and iteration techniques, a set of bounds for the macroscopic (effective) longitudinal elastic constants of the composites (including the simple lower arithmetic average estimate for longitudinal Young modulus Eeff ≥ EV) are constructed. Numerical examples are provided to illustrate the obtained results.

中文翻译：

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横向各向同性单向复合材料纵向弹性常数的最小能量界

我们考虑 n 分量横向各向同性单向弹性复合材料，其纵轴平行于横向各向同性分量的纵轴以及它们之间圆柱相边界的发生器。从最小能量和互补能量原理出发，结合适当的恒应变和分段恒应力试验场、优化和迭代技术，一组复合材料宏观（有效）纵向弹性常数的界限（包括简单的下算术平均值）纵向杨氏模量的估计值 Eeff ≥ EV) 被构建。提供了数值例子来说明所获得的结果。