cratepy.tensor.tensoroperations.derivative_isotropic_tensor

derivative_isotropic_tensor(mode, x)

Derivative of isotropic tensor-valued function of symmetric tensor.

The computational implementation to compute the derivative of an isotropic tensor-valued function of a symmetric tensor follows the Appendix A of Computational Methods for Plasticity [1].

[1]

de Souza Neto, E. A., Peri, D., and Owen, D. R. J. (2008). Computational Methods for Plasticity. John Wiley & Sons, Ltd, Chichester, UK (see here)

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Parameters:

• mode ({'log', 'exp'}) – Scalar function with single argument associated to the symmetric tensor-valued function (particular classe of isotropic tensor-valued functions).

• x (numpy.ndarray (2d)) – Second-order tensor at which isotropic tensor-valued function is evaluated.

Returns:

y – Derivative of isotropic symmetric tensor-valued function evaluated at x.

Return type:

numpy.ndarray (4d)