Defining Cracks

This section explains how to add explicit cracks to an MPM simulation.

Introduction

The extension of MPM to model explicit cracks is called CRAMP for CRAcks in the Material Point Method. The commands is this section are used to define the explicit cracks (and there can be any number of them). In addition, whenever a simulation has cracks you can use various crack settings commands to customize the features of the crack physics and set various material fracture properties.

The development of CRAMP is described first in a paper by Nairn (2003) (and its development was done using NairnMPM). Some other papers discuss calculation of J integral and stress intensity factor,, propose energy balance propagation, handle cracks in 3D (although not currently available in NairnMPM), use cracks to model imperfect interfaces,, and use traction laws with cracks. Some applications of using cracks in MPM include wood fracture, use of cracks to model glue bods in oriented strand board, simulation of dynamic fracture, and simulation of crack growth with fiber bridging.

Crack Definition Commmands

In CRAMP, a crack is defined as series of massless particles connected by crack segments. The first particle is the "start" tip and the last particle is the "end" tip. When CRAMP is active, nodes around the crack will be divided into two velocity fields to separately model motion of particle "above" the crack and "below" the crack. You define a crack by providing the points along the crack - (x₁,y₁) to (x_n,y_n). In addition, CRAMP fully accounts for crack contact, can model cracks with frictional contact, can use cracks to model imperfect interfaces, and can insert traction laws to model cohesive zones. When defining cracks, some additional are used to set crack contact mechanics, set crack tip materials, and insert traction laws.

In scripted files, a single crack is started with a NewCrack command, which is followed by one or more of the other commands to complete the crack definition:

NewCrack
GrowCrack
GrowCrackLine
GrowCrackArc
Friction
CrackInterface
CrackThickness

In XML files, each crack is defined in a CrackList element:

<CrackList friction='0.1' Dn='200' Dnc='-1' Dnt='200' Dt='5'>
  <pt units='mm' x='50.5' y='0' tip='1'/>
  <pt x='53' y='0'/>
     .
     .
     .
  <pt x='100.5' y='0'/>
  <Line xmin="102" ymin="0" xmax="130" ymax="10" resolution="5"
           start_tip="1" end_tip="1"/>
  <Circle xmin="102" ymin="0" xmax="130" ymax="10" resolution="10"
           start_tip="1" end_tip="1" start_angle="0" end_angle="90"/>
  <Thickness>1.0</Thickness>
</CrackList>

The commands and their functions are:

• NewCrack command - this command starts a new crack (in XML files, the <CrackList> element starts the crack.
• GrowCrack, GrowCrackLine, and GrowCrackArc commands - this commands extend the crack (the corresponding XML commands are <pt>, <Line>, and <Circle>).
• Friction and CrackInterface commands - these commands set the crack contact properties.
• CrackThickness command - this commands sets the crack thickness (the corresponding XML command is <Thickness>).

Starting the Crack

In scripted files, crack is started with the NewCrack command:

NewCrack (x1),(y1),<(mat)>,<(frict)>,<(tract)>

where

• (x1),(y1) - defines the start of the crack with crack tip (the coordinates are (R,Z) if axisymmetric).
• (mat) - this optional parameter can be one of three things:
  1. It can be used to define a material ID for the material at the start of the crack. Crack propagation is only possible when one or both of its crack tips have a material ID. If the material ID is omitted, the MPM calculations will correctly model that crack, but no propagation or fracture parameter calculations will occur.
  2. It can be "exterior" to indicate a crack to the edge of the body.
  3. It can be "fixed" to indicate a fixed crack. A fixed crack will not translate with the object and will not track surfaces. It can calculate J Integral but not Stress Intensity factor. It is useful when using cracks to create surfaces in an object. The surface can change by propagating the crack at constant crack speed initiated by critical J or by initiation time (see steady state propagation).
• (frict) - this optional parameter can specify a custom contact law for this crack. This option lets each crack have a different contact law such as different coefficients of friction. See the Friction Command for options in setting the contact law. If you want to set a contact law on a non-fixed crack, but do not want to define a tip material in parameter #3, you can enter parameter #3 as free, and then enter optional #4.
• (frict) and (traction) - alternatively, the optional #4 and #5 parameters can assign a traction law to the initial crack tip. To use this option, set #4 to traction and #5 to a material ID for a traction law material. The traction law will applied only to the first crack particle. To continue the traction law along the crack, use the traction law options in subsequent GrowCrack, GrowCrackLine and GrowCrackArc commands.