Friction

Both explicit cracks and multimaterial mode MPM can model frictional contact between the surfaces.

Introduction

Contact mechanics between surfaces can be model as frictionless sliding, Coulomb friction with a coefficient of friction, or stick contact (no sliding). In frictionless sliding, the tangential surface force is zero while the normal forces is determined by the amount of contact. In frictional sliding, the magnitude of the tangential force is related to the magnitude of the normal force by:

      [math]\displaystyle{ f_t = \mu f_n }[/math]

where μ is the coefficient of friction. But, if the induced tangential force from surface motion is less than this value (e.g., because f_n is low) then the contact is modeled as stick contact instead. In stick contact, the two surfaces move in the center-of-mass velocity field as if there were one material, but only as long as they remain in contact.

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.

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

Friction (frict)

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

<Friction>(frict)</Friction>

The meaning of (frict) is described below.

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

FrictionMM (frict)

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>(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. 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 Friction or Interface 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 custom (frict)=single for some material pairs; furthermore, the (frict)=single option is rigorous for nodes with two materials, but only approximate for nodes with three or more materials. In contrast, sharing velocity fields is accurate for any number of shared materials near a single node.

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.