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.

Contact without friction.

Contact without friction where penalty can depend on the gap.

No TM dependency here!

An evolution function must be associated to PEN_NORMALE (depending on generalized displacements GD).

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

Sticking contact where penalty can depend on the gap.

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.

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.

Tresca's friction law. Friction do not depend on pressure. It is computed 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

The threshold is usually computed 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.

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.

Not tested in 3D

Sticking thermomechanical contact

Not tested in 3D

Thermomechanical contact using Coulomb's friction law

Not tested in 3D

Thermomechanical contact using Tresca's friction law

The threshold is usually computed 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