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 laws give the sliding shear traction, S_slide, as a function of the normal traction, N, the contact area, A_c, the relative sliding velocity, 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 and Smith (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 Coulomb friction with adhesion

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 (T_N and T_S) are set to be functions of the normal and shear crack opening displacements (δ_N and δ_S. In other words:

      [math]\displaystyle{ T_N = f_N(\delta_N,\delta_S) }[/math]

      [math]\displaystyle{ T_S = f_S(\delta_N,\delta_S) }[/math]

The various imperfect interface laws differ by their options for the traction functions (f_N and f_S).

1. 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.
2. The numerical modeling of imperfect interfaces with linear traction-displacement discontinuity relations is described in a reference by the developer of NairnFEAMPM.

Modeling of imperfect interface by multimaterial contact is described in a paper by Nairn (2013).

1. 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.

Name	Number	Description
IgnoreContact	60	ignore contact or revert to single material mode
LinearInterface	6s	imperfect interface with tractions linear in interfacial separations