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.[1] 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 laws 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).
Traction laws have several uses. The most common is to implement cohesive zones where the traction laws will naturally debond if the critical opening displacements are reached. When they are modeling cohesive zones, the visualization tools can plot total crack length or debonded crack length (which is length with no traction laws). 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 transtion from debonded crack into the traction zone.
This section explains the possible traction laws. See the crack creation and crack propagation commands for how to use traction laws on cracks.
The use of traction laws on MPM cracks is described in Nairn (2009)[2] and used in Bardenhagen et al. (2011)[3] and Matsumoto and Nairn (2012).[4]
Define a Traction
You create traction law materials using a Material command block. Within that block all traction properties are set using property commands. Refer to each traction law type to learn about its possible properties.
Traction Law Materials
This table lists the available traction law materials. Click each one for more details and information on their properties.
| Name | ID | Description |
|---|
References
- ↑ J. A. Nairn, "Material Point Method Calculations with Explicit Cracks," Computer Modeling in Engineering & Sciences, 4, 649-664 (2003). (See PDF)
- ↑ J. A. Nairn, "Analytical and Numerical Modeling of R Curves for Cracks with Bridging Zones" Int. J. Fracture, 155, 167-181 (2009). (See PDF)
- ↑ S. G. Bardenhagen, J.A. Nairn, and H. Lu, "Simulation of dynamic fracture with the Material Point Method using a mixed J-integral and cohesive law approach," Int. J. Fracture, 170, 49-66.
- ↑ J.A. Nairn, "Fracture Toughness of Wood and Wood Composites During Crack Propagation," Wood and Fiber Science, 44, 121-133 (2012).