Constitutive Matrix

The relationship between the stresses \(\boldsymbol{\sigma}\) and the strains \(\boldsymbol{\varepsilon}\) is governed by the constitutive law – written in Voigt notation

\[\boldsymbol{\sigma} = \boldsymbol{C} \boldsymbol{\varepsilon},\]

where the so-called constitutive matrix \(\boldsymbol{C}\) links the strain \(\boldsymbol{\varepsilon}\) to the stress \(\boldsymbol{\sigma}\). In a two dimensional domain under plane stress conditions the constitutive matrix for an elastic body is defined via

\[\begin{split}\boldsymbol{C} = \dfrac{E}{1 - \nu^2} \begin{bmatrix} 1 & \nu & 0 \\[1ex] \nu & 1 & 0 \\[1ex] 0 & 0 & \dfrac{1 - \nu}{2} \end{bmatrix},\end{split}\]

where \(E\) is the Young’s modulus and \(\nu\) is the Poisson’s ratio.

Element.constitutive_matrix()

Return the constitutive matrix of the element.

Returns:The constitutive matrix of the element. Return type:numpy.ndarray