Auxetics among Two-Layered Composites Made of Cubic Crystals. Analytical and Numerical Analysis

The results of calculations of the effective Young's modulus of longitudinally stretched two-layered plates made of identically oriented cubic crystals are presented on the basis of analytical analysis and the numerical finite element method. Analytical dependences of effective Young's modulus on Young's moduli and Poisson's ratios of crystals in layers are presented. Combinations of pairs of crystals with a significant deviation of the effective characteristics from ones found by the rule of mixtures are determined. The dependences of the effective Young's moduli on extreme values of the Young's moduli and Poisson's ratios of crystals in layers are established. They are presented graphically, and in some cases are reflected in the form of a table.

Automated summary

The results of calculations of the effective Young's modulus of longitudinally stretched two-layered plates made of identically oriented cubic crystals are presented. The analytical dependences between the effective Young's modulus and the Young's moduli and Poisson's ratios of crystals in layers are discussed. Deviations from the rule of mixtures are found and the relationships between the effective Young's moduli and extreme values of the Young's moduli and Poisson's ratios of crystals in layers are established and presented graphically or in tabular form.