17.4 Elasticity Matrices

For the uni-axial approximation the elasticity matrix is equal to the identity matrix multiplied by the Youngs modulus. The dimensionality of the identity matrix is equal to the problem dimensioanlity.

For the plane stress approximation the matrix is

$$\frac{E}{1 - \nu^2} \; \begin{bmatrix} 1 & \nu & 0 & 0 \\ ... ... 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & (1-\nu)/2 \end{bmatrix}$$

For the plane strain approximation the matrix is

$$\frac{E}{(1 + \nu)(1-2\nu)} \; \begin{bmatrix} 1-\nu & \nu ... ... \nu & \nu & 0 & 0 \\ 0 & 0 & 0 & (1-2\nu)/2 \end{bmatrix}$$

For the axi-symmetric approximation the matrix is

$$\frac{E}{(1 + \nu)(1-2\nu)} \; \begin{bmatrix} 1-\nu & \nu ... ...nu & \nu & 1-\nu & 0 \\ 0 & 0 & 0 & (1-2\nu)/2 \end{bmatrix}$$

For the three dimensional approximation the matrix is

$$\frac{E}{(1 + \nu)(1-2\nu)} \; \begin{bmatrix} 1-\nu & \nu ... ...-2\nu)/2 & 0 \\ 0 & 0 & 0 & 0 & 0 & (1-2\nu)/2 \end{bmatrix}$$