(1) Introduction
(2) Origins

DESCRIPTION
(3) Generic characteristics
(4) Distinct characteristics
 

"IIIR" - type "IIIL" - type "OOO" - type "IIO" - type "OOI" - type

(5) Colored illustrations
 

"IIIR" - type "IIIL" - type "OOO" - type "IIO" - type "OOI" - type

(6) Photographs of models
 

"IIIR"- type "IIIL" - type "OOO" - type "IIO" - type "OOI" - type

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In Fig. -1(a),
The 3D-woven structure is shown to be
created as an interweavement of
(3) mutually perpendicular groups of elements.
The structure so formed is represented schematically by the cube.

In Fig. -1(b),
the structure is shown by itself,
still represented schematically by the cube.

In Fig. -2,
the structure is shown again, in the center of the fig.
As shown,
the structure can be regarded - in (3) distinct manners - as a "stack" of sections;
by showing the stack in expanded fashion, these sections can be shown separately.
The sections are shown schematically, as is the structure.

In Fig's. -3(a) thru -7(a),
these sections are shown pictorially.
So shown, each section
reveals that its structure is that of a simply woven fabric.

Also revealed in each of these sections:
the elements perpendicular to that fabric, penetrating through it.
They penetrate through it because
they penetrate through the entire stack of fabrics containing that fabric.
Doing so, these elements can be called the "transits" of that stack.
(Only the cross-sections of these transits are shown.)

In Fig's. -3(b) thru -7(b),
the structures themselves are represented pictorially,
in each case only showing only a small portion of the respective structure,
corresponding to the top-front corner of the schematic cube.

With the foregoing information,
it is possible to define
each of the (5) structures generically
in the following "generic description:"

          ===============================
          "The structure is so constructed that
           each section, in all (3) stacks,
           consists of a simply woven fabric".
          ===============================

Conclusion:
some guides to structural analysis.

When regarding Fig. -3(a) of
each of the (5) 3D-woven structures,
and in each case
clicking thru to "Larger View (a)",
the following structural characteristics can be illucidated.

(1)
=======

(a)
When regarding the top stack,
the structure can be understood as
consisting of red-green fabrics,
stitched together by black transits.

(b)
When regarding the left stack,
the structure can be understood as
consisting of black-green fabrics,
stitched together by red transits.

(c)
When regarding the right stack,
the structure can be understood as
consisting of black-red fabrics,
stitched together by green transits.

(a), (b), (c) are simultaneously valid,
and hence these weavements are indeed
isotropic along (3) mutually perpendicular axii.


(2)
=======

(a)
When regarding the top- and left stacks,
and also the schematic cube,
it can be determined that:
each green element is simultaneously
a constituent element of (1) red-green fabric and
a constituent element of (1) black-green fabric.
These fabrics* thus have that element common and
they interlace thru each other @ 90 degr. in
the location of that element.

(b)
When regarding the left- and right stacks,
and also the schematic cube,
it can be determined that:
each black element is simultaneously
a constituent element of (1) black-green fabric and
a constituent element of (1) black-red fabric.
These fabrics* thus have that element common and
they interlace thru each other @ 90 degr. in
the location of that element.

(c)
When regarding the right- and top stacks,
and also the schematic cube,
it can be determined that:
each red element is simultaneously
a constituent element of (1) black-red fabric and
a constituent element of (1) red-green fabric.
These fabrics* thus have that element common and
they interlace thru each other @ 90 degr. in
the location of that element.

Thus it can also be stated that
in the case of these 3D-weavements,
each element is "doubly interwoven" to become
a shared constituent element of (2) interlaced fabics*.

*Since these (2) fabrics have (1) constituent element in common,
 there is -strictly speaking- only (1) complete fabric; it is
 "either the one or the other".

(a), (b), (c) are simultaneously valid,
which further manifests the
tri-axial isotropy alluded to previously.