# Friction

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Both explicit cracks and multimaterial mode MPM can model contact between surfaces using a variety of contact laws.

## Introduction

The contact between materials or between crack surfaces can be modeled by selecting any of the available contact laws. When contact is activated and the surfaces are in contact, the tangential traction, S, is change to some function of normal force, N, and possibly other parameters of the various contact laws. For example, Coulomb friction will set tangential traction to

$\displaystyle{ S = \mu N }$

where μ is the coefficient of friction. But, if the induced tangential traction from surface motion is less than this value (e.g., because N is low) then the contact is modeled as sticking together instead.

## Setting Frictional Contact Properties

The commands below set default frictional properties for all cracks and/or default frictional properties for all material-material contact in multimaterial MPM. If needed, you can always customize each crack or each material-material pair to have their own frictional properties. The basic process is to define one or more contact law and then use the commands below to assign those laws to various contact mechanics tasks.

### Friction on Explicit Cracks

Explicit cracks in NairnMPM can model frictional contact. To choose the default frictional contact options for cracks in scripted files, use the command

ContactCracks (lawID)


In XML files, the default frictional contact properties for cracks are defined with a <Friction> command within the <Cracks> element in the <MPMHeader>:

<Friction law='(lawnum)'/>     or     <Friction lawname='(lawID)'/>


where (lawID) is the ID of the desired frictional contact law. In XML files, the contact law can also by selected by number (in (lawnum)) or name (but not both).

The above commands set the default frictional contact properties for crack surfaces. When a simulation only has only one crack, this setting is enough. For simulations with more than one crack, you can set different frictional properties for each crack, or convert some cracks to imperfect interfaces.

### Friction in Multimaterial MPM

Contact in multimaterial mode MPM can model frictional contact. To choose the default frictional contact options for material-material contact in scripted files, use the command

ContactMM (lawID)


In XML files, the default frictional contact properties for material contact are defined with a <Friction> command within the <MultimaterialMode> element in the <MPMHeader>:

<Friction law='(lawnum)'/>     or     <Friction lawname='(lawID)'/>


where (lawID) is the ID of the desired frictional contact law. In XML files, the contact law can be selected by number (in (lawnum)) or name (but not both).

The above commands set the default frictional properties for contact between any two materials. When a simulation only has two materials contacting by friction, this setting is enough. For simulations with more than two materials, you can set different frictional properties for each material pair, or even combine material pairs interacting by friction with those connected by an imperfect interface, by using a Contact material property for the secondly-defined material of each pair needing different contact mechanics.

For multimaterial mode simulations with more than two materials where some contact by friction or imperfect interfaces and others should move together in single velocity fields, you can use the shareMatField property in materials that should share the same field. This approach is more efficient than using "stick" contact law for some material pairs.

## Frictional Heating

When doing simulations that include conduction calculations, you can optionally convert the work of frictional sliding into heat. Two options are available that can be used to activate heat conversion for frictional sliding between crack surface and/or for friction sliding in multimaterial contact. To track the total amount of friction heating, the simulation can choose Friction Work in the global archiving options.

Frictional heating was improved in Fall 2015 (in OSParticulas) and in January 2016 (in NairnMPM) to use a second order method.[1] The new method can be observed to converge faster, especially in simulations with high contact forces and vibrations.

## Deprecated Friction Commands

Contact laws were implemented in NairnMPM (January 2016) and OSParticulas (revision 695). Prior to this new feature, frictional contact was limited to simple Coulomb friction the coefficient of friction was entered differently. This section documents the deprecated commands. They still work, but command files should be convert to the new methods documented above.

### Friction on Explicit Cracks (Deprecated)

In scripted files, default frictional contact for cracks was set using

Friction (frict)


In XML files, the default frictional contact properties for cracks was defined with a <Friction> command within the <Cracks> element in the <MPMHeader>:

<Friction>(frict)</Friction>


The meaning of (frict) is described below.

### Friction in Multimaterial MPM (Deprecated)

In scripted files, the default frictional contact for material-material contact was set using

FrictionMM (frict)


In XML files, the default frictional contact properties for material contact was defined with a <Friction> command within the <MultimaterialMode> element in the <MPMHeader>:

<Friction>(frict)</Friction>


where (frict) defines the type of friction:

• (frict)=(zero or positive number) or (frict)=none - crack contact is by friction with the supplied coefficient of friction. Enter zero (or "none") for frictionless sliding.
• (frict)=stick (or a number between -1 and -9) - crack contact by stick conditions. When in contact, the two materials contact by non-slip (or stick) conditions (which means they both use the center of mass velocity), but when not in contact, they move separately.
• (frict)=ignore or (frict)=single (or a number less than -10) - ignore crack contact when modeling friction on cracks or revert to single velocity field when modeling material contact in multimaterial MPM. This setting will give poor results for cracks that are in contact. Using this setting for all multimaterial mode contact is not the same as turning off multimaterial mode. It is the same for only two materials, but discrepancies will occur when some nodes see three or more materials.

Note that XML files must always use the numeric option instead of of the text settings.

The above commands set the default frictional properties for contact between any two materials. Custom friction (or conversion to imperfect interface contact) was done using a Friction or Interface material property for the secondly-defined material of each pair needing different contact mechanics.

## Notes

1. If you use both law and lawname attributes in the same XML command, the lawname is used to select the law.
2. Note than an XML file can reference materials by name or number, but not mix these methods. The Friction command should therefore always refer to contact law materials by the same method that other material commands are using reference materials (in that same XML file).

## References

1. J.A. Nairn and G. S. Smith (2016) "Generalized Contact and Improved Friction Heating the Material Point Method," in preparation.