# The Chaboche mechanical model¶

## Deterministic model¶

The Chaboche mechanical law predicts the stress depending on the strain:

where:

• is the strain,

• is the stress (Pa),

• , , are the parameters.

The variables have the following distributions and are supposed to be independent.

Random var.

Distribution

Lognormal ( MPa, MPa)

Normal ( MPa, MPa)

Normal (, )

Uniform(a=0, b=0.07).

## Parameters to calibrate¶

The vector of parameters to calibrate is:

We set:

• ,

• ,

• .

## Observations¶

In order to create a calibration problem, we make the hypothesis that the strain has the following distribution:

Moreover, we consider a gaussian noise on the observed constraint:

and we make the hypothesis that the observation errors are independent. We set the number of observations to:

We generate a Monte-Carlo samplg with size :

for . The observations are the pairs , i.e. each observation is a couple made of the strain and the corresponding stress.

## Thanks to¶

• Antoine Dumas, Phimeca

## References¶

1. Lemaitre and J. L. Chaboche (2002) “Mechanics of solid materials” Cambridge University Press.

>>> from openturns.usecases import chaboche_model as chaboche_model