`-crack <I|II|III> <stress|strain> <`

*K _{s}*> <p

This option inserts a straight crack in the system. The equations used by this option can be found e.g. in L.B. Freund, *Dynamic fracture mechanics*.

The user has to provide the following parameters:

**I|II|III**: mode of the crack, must be I (opening), II (in-plane shear) or III (out-of-plane shear).**stress|strain**: decides if the crack is built assuming plane stress or plane strain, respectively.: stress intensity factor (in GPa.Å*K*_{s}^{1/2}).**p**: coordinates of the crack in the plane normal to the crack tip line (see ξ below), by order of permutation X, Y, Z: if ξ=Z then p_{1}, p_{2}_{1}is the position along X and p_{2}the position along Y; if ξ=Y then p_{1}is along Z and p_{2}along X; if ξ=X then p_{1}is along Y and p_{2}along Z. The positions <p_{1}> and <p_{2}> are usually given in Å. It is also possible to give them with respect to the box dimensions with the keyword BOX and an operation (see this page).**ξ**: direction of the line of the crack tip, must be x, y or z.**n**: direction normal to the plane of cut (also normal to the surfaces forming the crack lips), must be x, y or z, and must be different from ξ.**μ**: shear modulus of the material (in GPa).**ν**: Poisson ratio of the material.

If plane stress is used then `κ=(3-ν)/(1+ν)`

; otherwise (i.e. assuming plane strain) `κ=3-4ν`

.

For a **mode I crack** (opening crack) the displacements applied to any atom in the system are:

`u`

_{x1} = (*K _{s}*/2μ) √

`u`

_{x2} = (*K _{s}*/2μ) √

where x_{3} is the direction <ξ> of the crack line, and x_{2} the normal to the plane of cut (i.e. x2=<n>),

is the distance of the atom to the crack tip, and *r*`θ`

is the angle between the plane normal to <n> and the segment formed by the atom and the crack tip. In addition for a mode I crack the box is elongated along x2 by `(`

.*K _{s}*/μ)√pos2/2π(κ+1)

For a **mode II crack** (in-plane shear crack) the displacements are:

`u`

_{x1} = (*K _{s}*/2μ) √

`u`

_{x2} = -(*K _{s}*/2μ) √

And finally for a **mode III crack** (out-of-plane shear crack):

`u`

_{x3} = (*K _{s}*/μ) √

In addition to these displacements, Atomsk also computes the theoretical (continuum) stresses associated with the crack and saves the Voigt components σ_{xx}, σ_{yy}, σ_{zz}, σ_{yz}, σ_{xz} and σ_{xy} as auxiliary properties for each atom.

In linear elastic materials a mixed-mode problem can be treated by using this option three times to add up the three contributions:

`u = u`

_{modeI} + u_{modeII} + u_{modeIII}

If a selection was defined (with the option `-select`

) then the displacements described above are applied only to selected atoms.

By default no crack is introduced at all.

`atomsk initial.xyz -crack I stress 20 30.0 0.5*BOX z y 90 0.3 crack.cfg`

This will read

`initial.xyz`

and insert a mode I crack along Z, assuming plane stress, the crack lips being normal to ξ=Y, using a stress intensity factor*K*=20 GPa.Å_{s}^{1/2}, a shear modulus μ=90 GPa and a Poisson ratio ν=0.3. The crack will be at X=30 Å and in the center of the box along Y. The result will be output to`crack.cfg`

.`atomsk initial.xyz -crack I stress 40 30 0.5*BOX z y 90 0.3 -crack II stress 10 30 0.5*BOX z y 90 0.3 -crack III stress 10 30 0.5*BOX z y 90 0.3 crack.cfg`

This will read

`initial.xyz`

and insert a crack by adding three contributions of modes I, II and III. The result will be output to`crack.cfg`

.