Modeling Material Symmetry - Continuum Mechanics of Anisotropic Materials - page 79

Fig. 4.4 Layers of fibers are
alternated to obtain a laminar
composite
forces for biological materials, method of formation for geological materials, and
method of manufacture for many manufactured materials. These factors are
discussed in the following paragraphs.
The selection of material symmetry for a model of a material depends upon the
intended application of the model. For example a common application of elasticity
theory is to steels that are employed in large objects for structures. In this applica-
tion steels are conventionally treated as materials with isotropic symmetry. The
basis for the isotropic symmetry selection is an RVE of a certain practical size that
averages over many grains of the microstructure. Although each crystalline grain is
oriented, their orientation is random and their average has no orientation, hence for
a large enough RVE the material is isotropic. However if the application of the
model is to study the interaction between the crystalline grains, a much smaller
RVE will be selected. If the RVE selected is entirely within a single crystalline
grain, then this RVE selection would imply cubic material symmetry since ferrous
materials are characterized by cubic symmetries. It follows that the selection of
different size RVE's can imply different material symmetries. The selection of a
particular size RVE is at the discretion of the person making the model, and that
selection should be determined by the model's intended use.
Man-made composite materials are often designed to be anisotropic because
their intended use is to carry a particular type of loading that requires stiffness and
strength in one direction more than in others. While many materials might have the
stiffness and strength required, a composite material may have a lesser weight.
A unidirectional fiber-reinforced lamina of a composite is illustrated in the top
panel of Fig. 4.4 . The directions of the fibers in alternate layers can be crossed to