OOF: Finite Element Analysis of Microstructures

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Subsections


zimmer and zimmer2

André Zimmermann asked for this element, so we put his name on it. It's a griffith element, but before it mutates it has hexagonal symmetry. It has the same problems that the griffith element does. See Section 4.5.11. Zimmer2 differs from zimmer in the same way that griffith2 differs from griffith: the zimmer element mutates if the total stored elastic energy exceeds the surface energy cost of a crack whereas the zimmer2 element mutates if the elastic energy due to the maximum principal stress exceeds the surface energy.

Parameters

orientation
The orientation of the hexagonal element before it mutates. If unrotated (orientation= 0), a hexagonal element is isotropic in the $xy$ plane (the plane of the screen), with the crystalline $c$-axis in the $z$ direction (out of the screen). See Section 4.3.

thermoelastic coefficients
Before mutation, the components of the stiffness matrix are those of the hexagonal element (Section 4.5.4): c11, c12, c13, c33, and c44. The two independent coefficients of thermal expansion are alpha11 and alpha33.

gamma
The surface energy of the crack.

knockdown1
The factor which multiplies the rotated stiffness matrix's $C_{zzzz}$ component during a mutation. [dimensionless]

knockdown2
The factor which multiplies the rotated stiffness matrix's remaining $C_{ijkl}$ components for at least one of ijkl=z during a mutation. [dimensionless]

only_once
If true, an element which has been damaged during one mutate command will not be damaged further on subsequent mutate commands. If false, the knockdown factors may be applied multiple times. Default: false

next up previous contents
Next: valeria Up: Element Types and their Previous: trigonalCrack   Contents
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