Traction Laws

Traction laws can be placed on crack surfaces to model cohesive zones.

Introduction

MPM implements explicit cracks by defining a series or massless particles that define the crack path. The method is called the CRAMP algorithm. The CRAMP algorithm takes care of the crack geometry and can handle crack-surface contact or imperfect interface contact. In addition, MPM can implement traction laws on the crack surfaces by assigning a traction law to one or more crack particles along the crack. The traction laws can be assigned when creating the crack or during crack propagation (i.e., new crack surfaces can be dynamically create traction laws). This section explains the possible traction laws. See the crack creation and crack propagation commands for how to use traction laws on cracks.

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 can assign a traction to any crack segments when creating the cracks. 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 conflict between contact and tractions, the crack surface contact must use frictionless 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. In addition, for planar 2D calculations you must specify the crack thickness using a Thickness command.

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 law can be assigned globally 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.

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).

Define a Traction

You create traction law materials using a Material command block. Within that block all material properties are set using property commands. Refer to each material type to learn about its possible properties.