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where
M
act
designates the set of all active plastic mechanisms. In the set of all
potentially active plastic mechanisms (
M
pact
), the active ones (
M
act
) are
M
pact
=
{a | f
a
=0}
[9.79]
{b ∈ M
pact
| λ
b
> 0}
M
act
=
[9.80]
In the case of multimechanism plasticity, when all mechanisms are active, a total
loading state is reached. In a partial loading state, only some of the mechanisms are
active. The elastic behavior takes place when none of the mechanisms are activated.
The strain rate is given as:
e
+
p
k
ε =
[9.81]
k
The active plastic multipliers are the solution to the following non-linear system of
equations obtained writing the consistency condition (
f
b
=0
)ofthe potentially active
mechanisms (
a, b ∈ M
pact
):
(Φ
b
: C :Ψ
a
−∂
α
b
f
b
:L
α
b
δ
ab
− ∂
η
f
b
: L
η
a
) λ
a
=Φ
b
:C:ε
[9.82]
a
∀a,b ∈M
pact
9.4. Parameter identification strategy for the ECP model
The essential ingredients of computational geotechnics are geotechnical data and
structure data in order to build the constitutive model and its parameters with emphasis
on aspects related to the validity and justification of the model for each application.
The particularity of the models we have presented is that they have been designed
to describe the behavior of geomaterials under a wide range of deformations. As a
result, a certain number of introduced parameters may not be into practice by certain
engineers. This difficulty is compounded by the fact that the required test results are
not always available. Furthermore, even when these tests are available, they may not
always be usable. For example, the model is based on the concept of critical state
and the parameters representing this state play a vital role. However, this critical
state is very difficult to reach; if particular precautions are not taken experimentally,
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