OOF: Finite Element Analysis of Microstructures

cubic next up previous contents
Next: hexagonal Up: Element Types and their Previous: empty   Contents

Subsections


cubic

These are elements with cubic symmetry. According to figure 4.2 there are three independent entries in the stiffness matrix. We pick those independent coefficients with a somewhat standard convention for the cubic Young's modulus ($E$), Poisson's ratio ($\nu$) and the anisotropy factor ( $A = 2C_{44}/(C_{11}-C_{12})$) which makes the $6\times6$ matrix form of $C_{ijkl}$ look like:

\begin{displaymath} \left( \begin{array}{cccccc} \ensuremath{\frac{E(1-\nu)}{(1+... ... & 0 & 0 &\ensuremath{\frac{A E}{2(1+\nu)}}\end{array}\right). \end{displaymath}

This is equivalent to the isotropic stiffness matrix when $A=1$.

The two-dimensional stiffness matrix depends on whether planestrain is true or false.

Parameters

young
The cubic Young's modulus $E$ [stress].

poisson
The cubic Poisson's ratio $\nu$ [dimensionless].

anisotropy
The anisotropy factor, $A$ [dimensionless].

alpha
The coefficient of thermal expansion. In cubic materials $\alpha_{11} = \alpha_{22} = \alpha_{33}$; all off-diagonal terms vanish. [inverse temperature]

orientation
The orientation of the crystalline axes. See Section 4.3. [degrees]


/* Send mail to the OOF Team *//* Go to the OOF Home Page */