utilities.py

computeCauchyGreenStrain(F):

Compute right Cauchy-Green strain tensor from deformation gradient.

Input Arguments

• F - deformation gradient in Voigt notation

Output Arguments

• C - Cauchy-Green strain tensor in Voigt notation

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computeJacobian(F):

Compute Jacobian from deformation gradient.

Input Arguments

• F - deformation gradient in Voigt notation

Output Arguments

• J - Jacobian

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computeStrainInvariantDerivatives(F,i,secondDerivative=False):

Compute derivatives of the invariants of the Cauchy-Green strain tensor with respect to the deformation gradient. Plane strain is assumed.

Input Arguments

• F - deformation gradient in Voigt notation

• i - specify the invariant that should be differentiated- I1, I2, I3, Ia or Ib

• secondDerivative - specify if second derivative should be computed

Output Arguments

• dIdF - derivative (note that the size of dIdF depends on the choice of secondDerivative)

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computeStrainInvariants(C):

Compute invariants of the Cauchy-Green strain tensor. Plane strain is assumed.

Input Arguments

• C - Cauchy-Green strain tensor in Voigt notation

Output Arguments

• I1 - 1st invariant

• I2 - 2nd invariant

• I3 - 3rd invariant

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getStrainPathDeformationGradient(strain_path, gamma_steps, gamma):

Generate deformation gradients based on a given strain path.

Input Arguments

• strain path - A two letter string defining one of the elementary strain strain_paths
• gamma - Gamma loading parameter for the deformation gradient.
• gamma steps - Specifies how many steps should be taken from F(gamma=0) to F(gamma=gamma)

Output Arguments

• F - Deformation gradient in Voigt notation.

• x-label - Label for plotting