Modeling Material Symmetry - Continuum Mechanics of Anisotropic Materials - page 78

4.3 Crystalline Materials and Textured Materials
The difference between the crystalline materials and the textural materials is the
difference between the types of force systems that determine the two different types
of symmetry. Crystallographic symmetries are determined by the internal force
systems that hold the material together in its solid form. These are force systems
between atoms or molecules. The lines of action of the attractive forces between
lattice points of a crystal determine the crystalline symmetry. On the other hand, the
symmetry of textured materials is determined mainly by external, rather than
internal, force systems. For example, it is well known that geological materials
have material symmetries associated with the stress state experienced by the mate-
rial during its formative state. Sedimentary deposits are generally organized by the
direction of gravity at the time of their formation. Similarly, the material symmetry
of structural steel is often determined by the external force systems associated with
its method of manufacture (extrusion, rolling, etc.) and not by the fact that it is
composed of ferric polycrystals. Man-made composites are generally designed to
survive in specific stress states and therefore can generally be considered as having a
material symmetry designed for the external force systems they will experience.
Plant and animal tissue are known to functionally adapt their local material structure
to external loads. In each of these examples the macroscopic material symmetry of
the textured material is determined by external force systems, even though at the
microscopic level some constituents may have crystalline symmetries determined
by internal force systems, as is the case with structural steel and bone tissue.
Crystals have the most clearly defined symmetries of all naturally occurring
materials. In crystallography an ideal crystal is defined in terms of a lattice.
A lattice is an infinite array of evenly spaced points that are all similarly situated.
Points are regarded as "similarly situated" if the rest of the lattice appears the same
and in the same orientation when viewed from them. An ideal crystal is then
defined to be an object in which the points, or atoms, are arranged in a lattice.
This means that the atomic arrangement appears to be the same and in the same
orientation when viewed from all the lattice points, and that the atomic arrangement
viewed from any point that is not a lattice point is different from the atomic
arrangement viewed from a lattice point. The form and orientation of the lattice
are independent of the particular point in the crystal chosen as origin. An ideal
crystal is infinite in extent. Real crystals are not only bounded, but also depart from
the ideal crystal by possessing imperfections. Forces that act on the lines connecting
the lattice points hold crystals together. The force systems that hold a crystal
together and give it shape and form are internal force systems.
Most large samples of natural materials are not crystals. They are either not
crystalline at all or they are polycrystalline. Polycrystalline materials are composed
of small randomly oriented crystalline regions separated by grain boundaries. The
material symmetry of these materials is not determined by the crystal structure of
their chemical components but by other factors. These factors include optional
design for man-made composite materials, growth patterns, and natural selection