ABSTRACT
It follows that cijkl=cklij, which implies that there are, at most, 21 distinct coefficients. There are no further arguments from general principles for fewer coefficients. Instead, the number of distinct coefficients is specific to a material, and reflects the degree of symmetry in the material. The smallest number of distinct coefficients is achieved in the case of isotropy, which can be explained physically as follows. Suppose a thin plate of elastic material is tested such that thin strips are removed at several angles and then subjected to uniaxial tension. If the measured stress-strain curves are the same and independent of the orientation at which they are cut, the material is isotropic. Otherwise, it exhibits anisotropy, but may still exhibit limited types of symmetry, such as transverse isotropy or orthotropy. The notion of isotropy is illustrated in Figure 6.1.
