Contact Laws

Introduction

NairnMPM and OSParticulas implement contact physics on crack surfaces and between materials in multimaterial mode to model friction or imperfect interfaces. The contact mechanics is determined by selecting a contact law. The currently available contact laws are divided into two types — frictional contact laws and imperfect interface laws. These default crack contact or for material-material contact are selected by using the ContactCracks or ContactMM commands. if needed, the default contact laws can be customized for each individual crack when defining a new crack or can be customized for each material pair by using the Contact material property. This section documents all the possible contact laws.

All contact laws are defined by using a Material command block. Within that block all contact law properties are set using property commands. Refer to each contact law type to learn about its possible properties.

Frictional Contact Laws

Frictional contact can be models with laws that give the sliding shear traction, S_slide, as a function of the normal traction, N, the contact area, A_c, the relative sliding velocity after imposition of contact law, Δv, and possibly other parameters, or:

      [math]\displaystyle{ S_{slide} = f(N,A_c,\Delta v,...) }[/math]

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

      [math]\displaystyle{ S_{resultant} = \min(S_{slide},S_{stick}) }[/math]

where S_stick is the shear traction needed for tangential motion of the two surface to move together (i.e., to stick). 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 S_slide, the surfaces will slide with the given sliding traction. More details on friction in MPM can be found in Nairn et. al (2016).

The available frictional contact laws are listed in the following table. See each law to learn about the function used to determine S_slide and about the parameters required to use that law.

Name	Number	Description
IgnoreContact	60	ignore contact or revert to single material mode
CoulombFriction	61	contact by simple Coulomb friction
AdhesiveFriction	63	contact by velocity-dependent Coulomb friction with adhesion
LiquidContact	64	from slip to stick contact for fluid flow

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 tangential tractions (T_n and T_t) are set to be functions of the normal and tangential displacement discontinuities ([u_n] and [u_t]). In other words:

      [math]\displaystyle{ T_n = f_n([u_n],[u_t]) }[/math]

      [math]\displaystyle{ T_t = f_s([u_n],[u_t]) }[/math]

The various imperfect interface laws differ by their options for the traction functions (f_n and f_s). More details on imperfect interfaces in MPM can be found in Nairn (2007) and (2013).

Note that whenever using imperfect interface modeling with cracks or in multimaterial mode, you must use the displacements method whenever the interface law has non-zero tangential traction. In other words, the simulation must omit the ContactPosition and/or ContactPositionCracks commands.

The available imperfect interface contact laws are listed in the following table. See each law to learn about the functions used to determine the interfacial tractions and about the parameters required to use that law. The NonlinearInterface described below actually implements a linear interface law, but it can be subclasses by programmers to create a custom imperfect interface material.

Name	Number	Description
IgnoreContact	60	ignore the interface or revert to single material mode with no interface
LinearInterface	62	imperfect interface with tractions linear in interfacial separations
NonlinearInterface	65	imperfect interface with tractions as a function of interfacial separations
DebondingInterface	65	imperfect interface with failure stresses for debonding