Transverse isotropy
The transverse isotropy is a special case of anisotropy. With the orthotropic materials transversely isotropic have in common is that there is no coupling between strains and shear strains. In addition, there is an excellent direction to which these materials can be rotated without changing its elastic properties. That is, perpendicular to this axis, the levels of elastic properties are independent of the direction ( isotropic level). In different planes oriented properties are direction-dependent.
Importance in the design
Unidirectional fiber-reinforced single layers, basic elements of composite materials are transversely isotropic with respect to their parallel fiber axis. The individual layers generally have strongly anisotropic ( direction-dependent ) properties. In the construction transversely isotropic materials are often used. They have the advantage of directional modules. However, the designer should not have to worry about changing the properties on rotation as long as he charged to the material in its symmetry axes.
Mathematical formulation
A transversely isotropic material is characterized in that in its stiffness or compliance matrix, the coupling terms are not occupied. Shear stresses do not lead to expansion. Furthermore, the direction-dependent elastic moduli reduce to two. Due to the transverse isotropy, the following expressions are identical:
Even though there are, as with orthotropic materials, the indices of the Poisson's ratios can not be exchanged, however, applies, so that overall the elasticity law on 5 independent variables reduced:
Symbols:
- Modulus of elasticity in the direction i
- Shear modulus in the ij - plane
- Poisson's ratio in the direction j (effect) when loading in the i direction (cause)
- , Normal stress and normal strain in direction i
- , Shear stress or shift in the i- plane in the direction j
The dimensions of the modules and voltages are force per unit area. The Poisson's ratios and the strains are dimensionless.