PREDICTION OF ELASTIC CONSTANTS AND THERMAL EXPANSION
photomicrographs. The estimates need not be very precise, since the knockdowns are
small in most systems (see Section 3). Thus ply properties in WEAVE are defined
without assuming periodicity. A similar code was reported in [5.26] for triaxial braids,
but it is not included in this edition of the handbook.
Nonperiodic, Nonlaminar Textile Composites
When a textile composite is nonperiodic and nonlaminar, a different approach
must be taken to describing its geometry. In the Binary Model (BINMOD), the axial
properties of yarns are represented by two-noded line elements, while the transverse
stiffness, shear stiffness, and Poisson’s effects are represented by solid “effective
medium” elements. Thus the tow architecture is represented by piece-wise straight line
segments in one-to-one correspondence with the positions of tow axes in the real
composite. Details of yarn cross-sectional shape and curvature over gauge lengths less
than the center-to-center tow spacing are omitted: by minimizing the degrees of freedom
in the model, much larger pieces of the textile composite can be simulated. Tow waviness
can be introduced by offsetting nodes on the tow elements in the stress-free configuration
of the model. There is in principle no restriction on the arrangements the tows may have
or any requirement of symmetry or periodicity. However, the code has been developed so
far to deal only with 3D interlock weaves.
Models such as the Binary Model appear to offer the best approach to modeling
integral textile structures (Section 2.4), which are nearly always nonperiodic and
nonlaminar. Neither are the tows in textile composites small relative to the external
dimensions expected in typical integral structures. Therefore, the representation of tows
as discrete entities would appear to be the minimum required level of detail.
5.2.3 Modeling Thermo-Elastic Properties
The approach to evaluating macroscopic stiffness tensors and coefficients of
thermal expansion once again naturally depends on whether a textile is classified as
quasi-laminar or nonlaminar. It is also useful to distinguish methods of analysis
according to the degrees of freedom permitted for local stress variations.
The Isostrain Approach (Orientation Averaging)
The isostrain assumption uses the lowest number of internal degrees of freedom
possible in elasticity calculations without introducing symmetry elements not present on
