# OOF: Finite Element Analysis of Microstructures

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##

griffith and griffith2

These elements are designed to fail (*i.e,* mutate (Section
3.1.4)) under the Griffith criterion, which states that a
crack will propagate when the total surface energy required to
propagate the crack can be supplied by the elastic energy stored in
the body:

(4.1) |

*OOF*the element size is used to specify the characteristic crack length and the volume of integration is the element area (per unit depth). In other words, the elastic energy is assumed to come entirely from the cracking element.

Because elements in *OOF* can't actually crack, after mutating the
elements reduce their moduli anisotropically to simulate a crack,
and the amount of surface area generated by mutation has to be
estimated. We take it to be the diameter of a circle with the same
area as the element.

CAUTION: Neither griffith nor griffith2 is a fully correct implementation of the Griffith criterion. griffith mutates when the stored elastic energy before mutation is greater than the surface energy after mutation, which doesn't account for the fact that there is still some elastic energy left in the element after it mutates. griffith2 solves this problem partially by not including energy due to stress perpendicular to the surface.

The process of mutation is similar to that for the damage element (Section 4.5.10):

- The energy balance for cracking is computed.
- If the energy balance is favorable for cracking, the direction of the maximum principle stress is found.
- Modfication of the stiffness matrix proceeds as in the damage element (Section 4.5.10).

### Parameters

*orientation*- As with the damage element, this is meaningless. See the explanation
in Section 4.5.10. [degrees]
*thermoelastic coefficients*- All thermoelastic coefficients for a undamaged damage element are
isotropic as described in section 4.5.1.
*gamma*- The energy per unit length of the crack
surface. [stress/length]
^{4.6} *knockdown1*- The factor which multiplies the rotated stiffness matrix's
component during a mutation. This should be a small number, if
the element is really to be ``cracked''. [dimensionless]
*knockdown2*- The factor which multiplies the rotated stiffness matrix's remaining
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`

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