Linear Elastic

Standard linear elastic material where a transversal anisotropy may be assigned to the elasticity matrix \(\mathbf{D}\).

Theory

The elasticity matrix \(\mathbf{D}\) can be written in term of the vertical oedometric compressibility \(C_{M}\) as:

\(\mathbf{D} = C_{M}^{-1} \begin{bmatrix} a_{11} & a_{12} & a_{13} & 0 & 0 & 0 \\ a_{21} & a_{22} & a_{23} & 0 & 0 & 0 \\ a_{31} & a_{32} & a_{33} & 0 & 0 & 0 \\ 0 & 0 & 0 & g_{1} & 0 & 0 \\ 0 & 0 & 0 & 0 & g_{2} & 0 \\ 0 & 0 & 0 & 0 & 0 & g_{3} \\ \end{bmatrix}\)

with:

\(a_{11} = \frac{\beta-\nu^{2}}{1-(\gamma\nu)^{2}}\)

\(a_{12} = \frac{\nu(\nu+\beta\gamma)}{1-(\gamma\nu)^{2}}\)

\(a_{13} = \frac{\nu}{1-(\gamma\nu)}\)

\(a_{33} = 1\)

\(g_{1} = \frac{\beta(1-\gamma\nu)-2\nu^{2}}{2(1-(\gamma\nu)^{2})}\)

\(g_{3} = \frac{g_{1}}{\theta}\)

The parameters involved are \(\nu=\nu_v\), \(\beta = E_H/E_Z\), \(\gamma= \nu_H/\nu_Z\), \(\theta = G_H/G_Z\), where \(E\) stands for the Young modulus, \(\nu\) for the Poisson modulus and \(G\) for the shear modulus, defined for horizontal \(H\) and vertical \(Z\) direction. The anisotropic linear elastic material assumes that \(C_{M}^{-1}\) is constant. Its value is given by the value in the depth-table \(C^{-1}_M(z)\) multiplied by a factor \(fact_{C_M}\) :

\(C_{M}^{-1} = fact_{C_M} C_{M}^{-1}(z)\)

Initialization

The initialization can be done using the tab_file or the restart file.

Input Notes

In the input file materials must be set:

• The material type MAT_TYPE = 1.

• The integer parameters MAT_IPAR[NI_MAT_TYPE] with NI_MAT_TYPE = 1:

• The real parameters MAT_RPAR[NR_MAT_TYPE] with NR_MAT_TYPE = 7: