Module 7: Micromechanics
  Lecture 34: Self Consistent, Mori -Tanaka and Halpin -Tsai Models
 


For example, in case of  for a circular fibres in a square array,   and for rectangular fibres cross section of length   and width   in a hexagonal array,    where    is in the direction of loading. Similarly, for  for circular fibres in a square array , and for rectangular cross-section with length   and width   in a hexagonal array,  , where   is in the loading direction.

Note: In case of transversely isotropic material in 23 plane, the constitutive relations are given as

(7.296)

and

(7.297)

Here, the moduli  and  refer to the values in the longitudinal or axial direction of straining and    and   refer to the values in transverse plane. Further, the Poisson’s ratios are defined as  and  under the uniaxial tensions in 1 and 2 directions, respectively.