The Chaboche mechanical model

Deterministic model

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

\sigma = G(\epsilon,R,C,\gamma) = R + \frac{C}{\gamma} (1-\exp(-\gamma\epsilon))

where:

  • \epsilon is the strain,

  • \sigma is the stress (Pa),

  • R, C, \gamma are the parameters.

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

Random var.

Distribution

R

Lognormal (\mu = 750 MPa, \sigma = 11 MPa)

C

Normal (\mu = 2750 MPa, \sigma = 250 MPa)

\gamma

Normal (\mu = 10, \sigma = 2)

\epsilon

Uniform(a=0, b=0.07).

The model can be used in two different contexts:

  • model calibration with observations where R, C and \gamma are parameters,

  • uncertainty propagation where R, C and \gamma are random variables.

Thanks to

  • Antoine Dumas, Phimeca

References

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

API documentation

class ChabocheModel(strainMin=0.0, strainMax=0.07, trueR=750000000.0, trueC=2750000000.0, trueGamma=10.0)

Data class for the Chaboche mechanical model.

Parameters:
strainMinfloat, optional

The minimum value of the strain. The default is 0.0.

strainMaxfloat, optional

The maximum value of the strain. The default is 0.07

trueRfloat, optional

The true value of the R parameter. The default is 750.0e6.

trueCfloat, optional

The true value of the C parameter. The default is 2750.0e6.

trueGammafloat, optional

The true value of the Gamma parameter. The default is 10.0.

Attributes:
dimint

Dimension of the problem, dim=4.

StrainUniform distribution

Uniform(strainMin, strainMax)

RLogNormal distribution

LogNormal().setParameter(ot.LogNormalMuSigma()([750.0e6, 11.0e6, 0.0]))

CNormal distribution

Normal(2750.0e6, 250.0e6)

GammaNormal distribution

Normal(10.0, 2.0)

inputDistributionJointDistribution

The joint distribution of the input parameters.

modelFunction

The Chaboche mechanical law. The model has input dimension 4 and output dimension 1. More precisely, we have \vect{X} = (\epsilon, R, C, \gamma) and Y = \sigma.

dataSample

A data set of size 10 and dimension 2 which contains noisy observations of the strain (column 0) and the stress (column 1).

Examples

>>> from openturns.usecases import chaboche_model
>>> # Load the Chaboche model
>>> cm = chaboche_model.ChabocheModel()
>>> print(cm.data[:5])
        [ Strain      Stress (Pa) ]
0 : [ 0           7.56e+08    ]
1 : [ 0.0077      7.57e+08    ]
2 : [ 0.0155      7.85e+08    ]
3 : [ 0.0233      8.19e+08    ]
4 : [ 0.0311      8.01e+08    ]
>>> print("Inputs:", cm.model.getInputDescription())
Inputs: [Strain,R,C,Gamma]
>>> print("Outputs:", cm.model.getOutputDescription())
Outputs: [Sigma]

Examples based on this use case

Calibration of the Chaboche mechanical model

Calibration of the Chaboche mechanical model

Generate observations of the Chaboche mechanical model

Generate observations of the Chaboche mechanical model

Create a process sample from a sample

Create a process sample from a sample