Earlier works treated oil shale as an isotropic material
, but this is not consistent with its real nature observed in different directions.
The undamaged compliance matrix of the isotropic material
can be expressed as follows:
We consider a homogeneous simple shear in the isotropic plane of a transversely isotropic material
Therefore, for isotropic materials
, cross effects may appear only between the first and the third terms.
Examinations of the failure criteria related to the ultimate fracture strength of isotropic materials
have led to the introduction of various theories.
Nevertheless we shall consider the membrane as a pseudoelastic isotropic material
in the biological sense  that the material properties of the membrane remain the same throughout the deformation process becoming anisotropic only during the development of aneurysm sac.
The tendon was modeled as a transversely isotropic material
with collagen fibers aligned in the longitudinal (loading) direction (Weiss et al.
A transversely isotropic material
behaves identically in all planes perpendicular to the axis of symmetry.
With an increase in the degree of anisotropy of the sphere's material (through an increase in the [beta] parameter) the vibration amplitude decreases more than with an order of magnitude (at [beta] > 50) in comparison with isotropic materials
The inner and outer layers of the shell are comprised of isotropic material
whereas the middle layer is assumed to be functionally graded Material properties of shell are represented by Young's modulus (E), Poisson's ratio ( ) and mass density.
The use of DTI data in conjunction with the transverse isotropic material
model is a novel method that has not been attempted so far because the material data available for brain tissue are mostly isotropic in character.
We will solve the asymmetric problem of heat conduction in a solid plane plate made from isotropic material
A model with isotropic material
properties and this values for Young's modulus and height would have the same characteristic of deformation under pure bending and pure tension as the woven fiber approach model with the 0[degrees]/90[degrees] fiber configuration.
For a homogeneous material, properties do not depend on the location, and for an isotropic material
, properties do not depend on the orientation.
Human osteonal bone is an example of a transversely isotropic material
because it has the same Young's modulus in all transverse directions, but has a higher Young's modulus in the longitudinal direction.