The elastic stress rate is
where
is the elastic modulus tensor (which is a
doubly symmetric tensor:
,
and
),
and
is the elastic strain rate.
See the plasticity section for a definition of the elastic strain rate.
For an isotropic material
with
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 ,
,
,
and
and the unique direction
in space (see group_materi_elasti_transverse_isotropy).
The other non-zero moduli follow from
,
,
and from the
double symmetry conditions.
The Lade nonlinear elasticity is a stress dependent model which typically is used to model the elastic behavior of granular materials. It can be combined with plastic models, by example with the di Prisco plasticity model for soils.
The stress rates are linked to the strain rates by the equation:
![]() |
(1) |
where the function
is
where
with pressure
and deviatoric stresses
.
The model contains three user specified constants ,
,
which need to be specified in the group_materi_elasti_lade record.
and
are defined by means of an isotropic unloading test, and
by means of
an unloading-standard-triaxial-compression test.
For example for a loose sand
,
,
.
See [6] for the details.