Minimum energy and iteration estimates for longitudinal Young's modulus and Poisson's ratio of transversely-isotropic unidirectional composites

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.