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### Table of Contents

# Contact materials

## Description

For all contact materials, a penalty along the normal direction and a depth at which contact is detected are required. Contact can be:

- positively unilateral (
`UNILATERAL_POSITIF`

), contact for $\mbox{gap} \geq 0$ (by default) - negatively unilateral (
`UNILATERAL_NEGATIF`

), contact for $\mbox{gap} \leq 0$ - bilateral (
`BILATERAL`

), contact for both $\mbox{gap} \geq 0$ and $\mbox{gap}\leq 0$

*Choice of depth at which contact is detected:* If the contact matrix is made of circles, the depth must be smaller than the smallest radius. If it is planar, the depth is arbitrary, but a large depth leads to a slow contact detection, when if the depth is too small some contacts can be missed.

## FrictionlessContactMaterial

#### Description

Contact without friction.

#### Parameters

Name | Metafor Code | Dependency | Default |
---|---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `TM` | |

Depth at which contact is detected | `PROF_CONT` | - | |

Type of contact | `TYPE_CONT` | - | `UNILATERAL_POSITIF` |

## FrictionlessVariablePenaltyContactMaterial

#### Description

Contact without friction where penalty can depend on the gap.

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `GD` |

No `TM`

dependency here!

An evolution function must be associated to `PEN_NORMALE`

(depending on generalized displacements GD).

## StickingContactMaterial

#### Description

Sticking contact. A penalty along the tangential direction is added.

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `TM` |

Penalty along tangential direction | `PEN_TANGENT` | `TM` |

Depth at which contact is detected | `PROF_CONT` | - |

Type of contact | `TYPE_CONT` | - |

## StickingVariablePenaltyContactMaterial

#### Description

Sticking contact where penalty can depend on the gap.

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `GD` |

Penalty along tangential direction | `PEN_TANGENT` | `GD` |

No `TM`

dependency here!

An evolution function must be associated to `PEN_NORMALE`

and/or `PEN_TANGENT`

(depending on generalized displacements GD). These function can be different.

## CoulombContactMaterial

#### Description

Coulomb's friction law. A tangential penalty, a coefficient of static friction (setting the maximal tangential force before sliding) and a coefficient of dynamic friction (setting the value of the sliding force) are required.

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `TM` |

Penalty along tangential direction | `PEN_TANGENT` | `TM` |

Depth at which contact is detected | `PROF_CONT` | - |

Coefficient of static friction | `COEF_FROT_STA` | `TM` |

Coefficient of dynamic friction | `COEF_FROT_DYN` | `TM` |

Type of contact | `TYPE_CONT` | - |

## TrescaContactMaterial

#### Description

Tresca's friction law. Friction do not depend on pressure. It is calculated using penalty method with sticking contact, and starts sliding once the tangential stress reaches a threshold entered by the user.

This law requires the use of `AREAINCONTACT`

= `AIC_ONCEPERSTEP`

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `TM` |

Penalty along tangential direction | `PEN_TANGENT` | `TM` |

Depth at which contact is detected | `PROF_CONT` | - |

Static frictional shear factor | `TRESCA_STA_M` | `TM` |

Dynamic frictional shear factor | `TRESCA_DYN_M` | `TM` |

Initial shear yield stress | `TRESCA_K` | - |

Type of contact | `TYPE_CONT` | - |

The threshold is usually calculated using $m\,\sigma_0\,/\sqrt{3}$ where *m* is Tresca's coefficient of friction and $\sigma_0$ is the tensile yield stress of the material.

## TmFrictionlessContactMaterial

Thermomechanical contact without friction.

The heat flux $q_{N}$ normal to the contact interaction (going out of the slave surface) is given by

$$q_{N} = h_c \left(p_{N} \right) \left(T^{S} - T^{M}\left(\bf{\xi}^{S}\right)\right), $$

where

- $p_{N}$ is the contact pressure,
- $T^{S}$ is the temperature of the slave node,
- $T^{M}\left(\bf{\xi}^{S}\right)$ is the temperature of a point on the master surface corresponding to the closest projection of the slave node on the master surface,
- $h_c$ is the thermal resistance under conduction.

This thermal resistance under conduction $h_c$ is modeled as

$$h_c \left(p_{N} \right) = h_{c0} \left(\frac{p_{N}}{H_v}\right)^{w}, $$

where

- $H_v$ Vickers's material hardness ,
- $w$ is an exponent,
- $h_{c0}$ is the nominal thermal resistance under conduction.

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `TM` |

Depth at which contact is detected | `PROF_CONT` | - |

Nominal thermal resistance | `CTM_H_NOMINAL` | - |

Exponent | `CTM_EXPONENT_E` | - |

Material hardness | `CTM_HARDNESS` | - |

Type of contact | `TYPE_CONT` | - |

Not tested in 3D

## TmStickingContactMaterial

Sticking thermomechanical contact

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `TM` |

Penalty along tangential direction | `PEN_TANGENT` | `TM` |

Depth at which contact is detected | `PROF_CONT` | - |

Nominal thermal resistance | `CTM_H_NOMINAL` | - |

Exponent | `CTM_EXPONENT_E` | - |

Material hardness | `CTM_HARDNESS` | - |

Type of contact | `TYPE_CONT` | - |

Not tested in 3D

## TmCoulombContactMaterial

#### Description

Thermomechanical contact using Coulomb's friction law

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `TM` |

Penalty along tangential direction | `PEN_TANGENT` | `TM` |

Depth at which contact is detected | `PROF_CONT` | - |

Coefficient of static friction | `COEF_FROT_STA` | `TM` |

Coefficient of dynamic friction | `COEF_FROT_DYN` | `TM` |

Nominal thermal resistance | `CTM_H_NOMINAL` | - |

Exponent | `CTM_EXPONENT_E` | - |

Material hardness | `CTM_HARDNESS` | - |

Type of contact | `TYPE_CONT` | - |

Not tested in 3D

## TmTrescaContactMaterial

#### Description

Thermomechanical contact using Tresca's friction law

#### Parameters

Name | Metafor Code | Dependency |
---|---|---|

Penalty along normal direction | `PEN_NORMALE` | `TM` |

Penalty along tangential direction | `PEN_TANGENT` | `TM` |

Depth at which contact is detected | `PROF_CONT` | - |

Frictional shear factor | `TRESCA_M` | `TM` |

Initial shear yield stress | `TRESCA_K` | `TM` |

Nominal thermal resistance | `CTM_H_NOMINAL` | - |

Exponent | `CTM_EXPONENT_E` | - |

Material hardness | `CTM_HARDNESS` | - |

Type of contact | `TYPE_CONT` | - |

The threshold is usually calculated using $m\,\sigma_0\,/\sqrt{3}$ where *m* is Tresca's coefficient of friction and $\sigma_0$ is the tensile yield stress of the material.

Not tested in 3D