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Contact Law Materials

MPM implements contact physics on crack surfaces and between materials in multimaterial mode by using contact laws. Each contact law can define frictional contact or describe an imperfect interface. Contact laws are assigned to crack and material surfaces by using the ContactCracks and ContactMM commands, by using the Contact material property, or by choosing a custom contact law in the NewCrack command. This section explains the possible contact laws.

A contact law is defined using a Material command. See that command for (matid) and (name) parameters and then use the (type) parameter to define the type of contact law. The current options for (type) (by name or number) are:

The Material command should be followed by lines that contain the contact law properties. Each property should be on a separate line and when the last property is specified, enter a line with the single Done Command. The various contact laws expect different properties.

More documentation on contact laws can be found in the OSUPDocs wiki. It is relatively easy to add more traction laws; contact the developer if you need one.

Frictional Contact Laws

Frictional contact laws give the sliding shear traction, Sslide, as a function of the normal traction, N, the contact area, Ac, and the relative sliding velocity (after imposing the contact law), Δv,or:

Sslide = f(N,Ac,Δv)

Given any frictional law, the shear traction applied at any node is given by:

Sresultant = min(Sslide,Sstick)

where Sstick is the shear traction needed for tangential motion of the two surface to move together. In other words, if the shear traction calculated for frictional sliding is greater than the traction required for surfaces to stick together, then the surface will stick. Once that sticking shear traction exceeds Sslide, the surfaces will slide with the given sliding traction.

Imperfect Interface Contact Laws

Imperfect interfaces can be modeled two ways — by using contact laws on explicit cracks or by using them in multimaterial mode MPM. When contacting surfaces are modeling an imperfect interface, the normal and shear tractions (TN and TS) are set to be functions of the normal and shear crack opening displacements (δN and δT). In other words:

TN = fNNT)
TS = fSNT)

The various imperfect interface laws differ by their options for the traction function (fN and fS).

See the OSUPDocs wiki for more details on modeling imperfect interfaces and meanings of interface parameters.

Notes

  1. Note that use of imperfect interface laws requires extrapolation of displacements (i.e., no ContactPosition command is used) whenever the traction law has non-zero tangential tractions.
  2. When an analysis has imperfect interfaces, you can track total interface energy using the global archiving methods. In an elastic analysis, the total strain energy is the sum of the strain energy and the interface energy.
  3. The numerical modeling of imperfect interfaces with linear traction-displacement discontinuity relations is described in a reference by the developer of NairnFEAMPM.
  4. Modeling of imperfect interface by multimaterial contact is described in a paper by Nairn (2013).
  5. Imperfect interfaces can also be modeling in FEA analyses by using interface elements in NairnFEA. FEA interfaces must be linear and thus cannot set different normal stiffnesses for tension and compression.

Contact Law that Ignores Contact

This law is not actually a contact law. This law ignores contact on explicit crack surfaces. For multimaterial contact, this law will revert to a single velocity field as if they was not a material interface. The law has no properties that can be set.

This law will give poor results for cracks that are in contact, unless those cracks never experience contact. For multimaterial mode simulations, this mode reverts to a single velocity field. For simulations with more than two materials where some contact by other contact laws and others should use single velocity fields, the better approach than using this law is to use the shareMatField (matID) in materials that should share the same field.

Coulomb Friction Contact Law

This law implements simple Coulomb friction law where

Sslide = µ N

and µ is the dynamic coefficient of friction. If the friction coefficient is entered as a negative number, then surfaces stick when in contact but move freely when separated. The properties for this law are:

If the optional static coefficient of friction is changed to a positive number, it must be greater than the dynamic coefficient. The sliding will begin when it overcomes the static frictional force, but thereafter will slide with the dynamic coefficient of friction.

Coulomb Friction with Adhesion Contact Law

This law implements Coulomb friction law with adhesion. If the surface are in contact, the frictional sliding force is

Sslide = Sa + (µ +kΔv)N

where Sa is the tangential adhesion strength and µ is the dynamic coefficient of friction, and k allows the dynamic coefficient of friction to depend linearly on sliding velocity. If the surfaces are not in contact, the surface continue to stick as long as:

(Sstick/Sa)2 + (N/Na)2 < 1

where Na is the normal adhesion strength. If this criterion is not met (or if either Sa or Na are zero), the surfaces move freely with zero tractions. The properties for this law are:

If the optional static coefficient of friction is changed to a positive number, it must be greater than the dynamic coefficient. The sliding will begin when sliding force overcomes the frictional force calculated from static coefficient and Δv=0, but thereafter will slide with force found using dynamic coefficient of friction and the velocity-dependent term.

Liquid Contact Law

This frictional contact law implements a friction-style law between liquid and a wall where contact shear is related to shear rate, viscosity, and a scaling factor to vary from stick to slip contact. The sliding traction is

Sslide = k η Δv

where k is a scaling factor (with units 1/length) and η is viscosity of a fluid (which may depend on shear rate). Note that k = 0 leads to zero sliding traction or pure slipe; k large approaches stick contact; all other values of k give partial-slip boundary conditions that depend on the liquid's viscosity and could be tailored to match experimental results. The properties for this law are:

Note that this contact law uses the viscosity provided by the entered LiquidPhase material for all contact situations.

Linear Imperfect Interface Contact Law

This law implements an imperfect interface with tractions that depend linearly on crack opening displacements, although slopes can be different in tension or compression:

TN = DntδN     when separated
TN = DncδN     when in contact
TS = DtδS

The properties are the three interface parameters:

In theory, the interface becomes perfect in either direction as the interface parameters approach ∞, but high values for stiffness make the problem numerically unstable (unless very small time steps are used). To make the interface perfect in any direction, set the stiffness to -1, instead of using a high stiffness. A common situation is to model the interface as perfect in compression but imperfect in tension, which is done be setting Dnt to any value and Dnc to -1.

Nonlinear Imperfect Interface Contact Law (Type=65)

This law implements an imperfect interface with tractions that depend on displacement discontinuities at the interface. It is currently the same as the linear interface law except the implementation is done differently. It is more approximate, but likely very close to linear law and possibly faster. The parameters are:

In the future, this law (or subclasses of this law) will add actual non-linear traction laws.