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Micromechanics Models for Mechanical Properties 67
by the average stresses and the average strains are identical to that done by the micro
stresses and micro strains.
The effective properties are defined in terms of the relations between the average
stresses and average strains over a representative volume. They can be obtained by
applying boundary conditions in equations (4.8) and (4.9) as follows.
Iso-strain method imposition of a prescribed homogeneous displacement-based
boundary condition in equation (4.8) to a representative volume yields the following
stress-strain relation:
{F} = [FiE} (4.10)
where
--
‘36
‘35
‘34 -- (4.1 1)
‘41 ‘42 ‘43 ‘44 ‘45 ‘46
where i7G and FG are the average stress and average strain components, respectively,
and Cj are the effective elastic stifhess constants.
Iso-stress method application of homogeneous boundary conditions in equation
(4.9) to a representative volume leads to the following stress-strain relation:
(4.12)
where
s33 --- 1
----
[SI= l”31 SI32 s34 s35 !36 (4.13)
’41 s42 ’43 ’44 ’45 sa
where S, are the effective elastic compliances.
For a representative volume element, with well-defined dimensions, of a composite
material, the effective properties produced by employing the homogeneous boundary
