Скачать или смотреть Number of Independent Elastic constants | Isotropic| Anisotropic| Orthotropic | BY ALOK JHA

BY ALOK JHA concept
we have seen the constitutive equations for various types of (that is, nature of) materials. There are 81 independent elastic constants for generally anisotropic material and two for an isotropic material.

Let us summarize the reduction of elastic constants from generally anisotropic to isotropic material.

For a generally anisotropic material there are 81 independent elastic constants.

With additional stress symmetry the number of independent elastic constants reduces to 54.

Further, with strain symmetry this number reduces to 36.

A hyperelastic material with stress and strain symmetry has 21 independent elastic constants. The material with 21 independent elastic constants is also called as anisotropic or aelotropic material.

Further reduction with one plane of material symmetry gives 13 independent elastic constants. These materials are known as monoclinic materials.

Additional orthogonal plane of symmetry reduces the number of independent elastic constants to 9. These materials are known as orthotropic materials. Further, if a material has two orthogonal planes of symmetry then it is also symmetric about third mutually perpendicular plane. A unidirectional lamina is orthotropic in nature.

For a transversely isotropic material there are 5 independent elastic constants. Plane 2-3 is transversely isotropic for the lamina

For an isotropic material there are only 2 independent elastic constants.