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Option: crack


-crack <I|II|III> <stress|strain> <Ks> <p1> <p2> <ξ> <n> <μ> <ν>


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:

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:

       ux1 = (Ks/2μ) √r/2π cos(θ/2) [κ - 1 + 2sin2(θ/2)]

       ux2 = (Ks/2μ) √r/2π sin(θ/2) [κ + 1 - 2cos2(θ/2)]

where x3 is the direction <ξ> of the crack line, and x2 the normal to the plane of cut (i.e. x2=<n>), r is the distance of the atom to the crack tip, and 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 (Ks/μ)√pos2/2π(κ+1).

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

       ux1 = (Ks/2μ) √r/2π sin(θ/2) [κ + 1 + 2cos2(θ/2)]

       ux2 = -(Ks/2μ) √r/2π cos(θ/2) [κ - 1 - 2sin2(θ/2)]

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

       ux3 = (Ks/μ) √r/2π sin(θ/2)

In addition to these displacements, Atomsk also computes the theoretical (continuum) stresses associated with the crack and saves the Voigt components σxx, σyy, σzz, σyz, σxz and σxy 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 = umodeI + umodeII + umodeIII

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.


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