Traction Laws
Crack-Surface Traactions
Any section of a crack may be assigned a traction law material to apply traction to the crack surface as a function of crack normal and shear opening displacments. You assign a traction to any created segments by adding a mat='n' attribute to any pt, Line, or Circle command, where n is the traction law material nummber. Alternatively, you can use a matnam = 'law name' attribute where 'law name' is the name of the traction law material (see Defining Materials for details on numbers vs. names). In addition, for planar 2D calculations you must specify the crack thickness using a Thickness command.
The traction law will naturally debond if the critical opening displacements are reached. The visualization tools can plot total crack length or debonded crack length. Their difference is the length of crack surface with traction law materials still bonded. The tools can also plot the opening and shear displacements at the actual crack tip or the traction zone tip nearest the crack tip.
For normal opening, traction laws only apply traction when a cracked is opened. The crack contact mechanics handles the case where the crack surfaces are in contact. For shear opening, the traction law applies forces in both directions. To avoid conflicts with these tractions, the crack surface contact must use frictionaless sliding. In fact any crack with traction laws will automatically convert to a frictionless crack regardless of settings you use for the crack's contact condition.
Besides creating cracks with traction laws, you can also assign traction laws to new crack surfaces that are created when a crack propagates. The propagation traction can be assigned globally in the MPM Header or specifically for a given material type. Since a crack that starts with no traction laws, but creates them when it propagates, will not automatically convert to a frictionless crack, you should be sure that all such cracks are setup to use frictionless crack contact.
Interacting cracks with traction laws are handled, but not validated well. All validation runs were done using non-interacting, traction-loaded cracks.
The use of traction laws on MPM cracks is described in Nairn (2009) and used in Bardenhagen et al. (2011) and Matsumoto and Nairn (2012).