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cannot be used to analyse variations of mechanical properties with some important
architecture parameters due to the introduction of oversimplified assumptions. On the
other hand, it is almost impractical to investigate experimentally the mechanical
properties of textile composites and their dependence on the major architecture
parameters because of their complexity in geometry and spatial organisation. Hence, it
is desirable to develop an analytical approach which is capable of modelling textile
composites at a micro geometry level, and predicting effectively the mechanical
properties and their dependence on major architecture parameters.
Finite element analysis (FEA) is a useful and versatile approach used by many
researchers to predict mechanical properties of composite materials. A number of FEA
models have been developed to evaluate the effects of various fibre architecture
parameters on the mechanical properties of textile composites.
It is not intended to present or even review in this book all micromechanics methods
that have been used or may be potentially useful for characterising 3D fibre reinforced
composite materials. Instead, this book aims to provide a brief description of selected
micromechanics modelling methods that have been proved to be useful for predicting
the in-plane mechanical properties of 3D composites.

4.2 FUNDAMENTALS IN MICROMECHANICS

4.2.1 Generalized Hooke’s Law
For an elastic anisotropic material, the generalized Hooke’s law is the linear stress-
strain relation as given by:
{d= [ck} (4.1)
where
io}= {Oil O22 O33 O23 O31 Ol2)7

kll ‘22 ‘33 ‘23 ‘31 ‘I2)T
‘1, ‘12 ‘I3 ‘I4 ‘15 ‘16
‘21 ‘22 ‘23 ‘24 ‘25 ‘26
‘31 ‘32 ‘33 ‘34 ‘35 ‘36
‘41 ‘42 ‘43 ‘44 ‘45 ‘46
‘51 ‘52 ‘53 ‘54 ‘55 ‘56
‘61 ‘62 ‘63 ‘64 ‘65 ‘66

where oij and are the stress and strain components, respectively, and C, are the
elastic stiffness constants. The stiffness matrix is symmetric from an energy
consideration. There are 21 independent constants out of the 36 constants. The above
equation can also be written in the form:

(4.3)