The elastic stress rate is
where Cijkl is the elastic modulus tensor (which is a
doubly symmetric tensor:
Cijkl=Cjikl,
Cijkl=Cijlk and
Cijkl=Cjilk),
and
is the elastic strain rate.
See the plasticity section for a definition of the elastic strain rate.
For an isotropic material
with E group_materi_elasti_young modulus and
group_materi_elasti_poisson ratio
(the remaining non-zero moduli follow from the double symmetry conditions).
For a transverse isotropic material the material has one unique direction (think of an material with fibers in one direction). Here we take 'a' as the unique direction; 'b' and 'c' are the transverse directions. The material is fully defined by Caaaa, Cbbbb, Caabb, Cabab and Cbcbc and the unique direction in space (see group_materi_elasti_transverse_isotropy). The other non-zero moduli follow from Ccccc=Cbbbb, Cacac=Cabab, Cbbcc=Cbbbb-2Cbcbc and from the double symmetry conditions.