Some formal inequalities restricting the macroscopic (effective) longitudinal elastic constants of the $n$-component transversely-isotropic unidirectional composites, based on the minimum energy and complementary energy principles with the help of appropriate constant strain and piece-wise constant stress trial fields and optimization techniques, have been established. Exploring further the possible longitudinal stress–strain modes, additional starting original bounds are derived leading to the new set of iteration bounds on both effective longitudinal constants, which broaden and improve upon the ones of the first set constructed earlier (Pham, 2020) for the composites with positive longitudinal Poisson’s ratio. Another new set of iteration bounds is constructed for the composites having negative longitudinal Poisson’s ratio. Illustrating numerical examples are presented for comparisons.

限制宏观（有效）纵向弹性常数的一些形式不等式 $n$基于最小能量和互补能量原理，借助适当的恒应变和分段恒应力试验场和优化技术，建立了-组件横向各向同性单向复合材料。进一步探索可能的纵向应力 - 应变模式，推导出额外的起始原始边界，导致两个有效纵向常数的新迭代边界集，这扩大并改进了早期构建的第一组（Pham，2020）的迭代边界。具有正纵向泊松比的复合材料。为具有负纵向泊松比的复合构造另一组新的迭代边界。给出了说明性的数字示例以进行比较。