Abstract :
The very complex, multi-level hierarchical
construction of textile composites and their structural
components commonly manifests via significant property
variation even at the macro-level. The concept of a
‘‘meso-volume’’ (introduced by this author in early
1990s) is consistently applied in this work to 3-D stress/
strain and failure analyses of 3-D woven composites at
several levels of structural hierarchy. The meso-volume
is defined as homogeneous, anisotropic block of composite
material with effective elastic properties determined
through volumetrically averaged 3-D stress and
strain fields computed at a lower (‘‘finer’’) level of
structural hierarchy and application of generalized
Hooke’s law to the averaged fields. The meso-volume
can represent a relatively large, homogenized section
of a composite structural component, a lamina in
laminated composite structure, a homogenized assembly
of several textile composite unit cells, a single
homogenized unit cell, a resin-impregnated yarn, a
single carbon fiber, even a carbon nanotube assembly.
When composed together, distinct meso-volumes constitute
a 3-D Mosaic model at the respective hierarchy
level. A multi-scale methodology presented in this
paper first illustrates 3-D stress/strain analysis of the
Mosaic unidirectional composite, computation of its
effective elastic properties and their further use in 3-D
stress/strain analysis of the Mosaic model of 3-D woven
composite Unit Cell. The obtained 3-D stress/strain
fields are then volumetrically averaged within the Unit
Cell, and its effective elastic properties are computed.
The predicted effective elastic properties of 3-D woven
composite are compared with experimental data and
show very good agreement. Further, those effective
elastic properties are used in 3-D simulations of threepoint
bending tests of 3-D woven composite; theoretical
predictions for central deflection show excellent
agreement with experimental data. Finally, a 3-D
progressive failure analysis of generic 3-D Mosaic
structure is developed using ultimate strain criterion
and illustrated on the 3-D woven composite Unit Cell.
The predicted strength values are compared to experimental
results. The presented comparisons of theoretical
and experimental results validate the adequacy
and accuracy of the developed material models,
mathematical algorithms, and computational tools.
