====== CNTCQ ======

===== Description =====

Constitutive law for unilateral contact with friction, for thin 3D shell elements.

==== The model ====

This law is used for mechanical analysis of unilateral contact with friction in 3D state for shells.\\

Contact can occur on both sides of shell.\\

A penalty method is chosen to represent the contact.\\

COULOMB behaviour is assumed,  with constant friction coefficient.

==== Files ====

Prepro: LCNTCQ.F \\
Lagamine: CNTCQ4.F

===== Availability =====

|Plane stress state| NO |
|Plane strain state| NO |
|Axisymmetric state| NO |
|3D state| YES |
|Generalized plane state| NO |

===== Input file ===== 

==== Parameters defining the type of constitutive law ====

^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 98|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|

==== Integer parameters ====

^ Line 1 (I5) ^^
|NINTV| Number of sub-step to calculate the contact |

==== Real parameters ====

^ Line 1 (5G10.0) ^^
|RIGP| Penalty coefficient on pressure, $K_p$ |
|RIGT| Penalty coefficient on shear, $K_{\tau}$ (default = RIGP) |
|FRTCN| COULOMB's coefficient = $\Phi$ |
|COHES| Cohesion parameter for Tresca's law = B |
|TAUMX| Maximum value imposed for shear stress |

{{ :laws:cntcq.png?400 |}}

===== Stresses =====

==== Number of stresses ====

3

==== Meaning ====

|SIG(1)| = p : Pressure |
|:::| > 0 in compression |
|SIG(2)| = $\tau$ : Shear |
|:::| > 0 according with local coordinates of shell |
|SIG(3)| = $\tau$ : Shear |
|:::| > 0 according with local coordinates of shell |

===== State variables =====

==== Number of state variables ====

6

==== List of state variables ====

|Q(1)|IELD: State of contact |
|:::|= -1 : No contact |
|:::|= 0 : No sliding (elastic state in Tresca law, $\rvert\rvert\tau\rvert\rvert$ = FRTCN.$p$+COHES) |
|:::|= 1 : Sliding (plastic state, always if FRTCN = 0 and TAUMX = 0) |
|Q(2)|ISEG: Number of foundation segment in contact |
|Q(3)|DIS: Penetration distance |
|Q(4)|ICONT: Index of contact |
|:::|= 0 : Contact if DIS < 0 |
|:::|= 2 : No contact b/c of normal consistency or b/c abs(DIS) > DMAX |
|:::|= 11, 12 or 13 (only for foundation with triangular segments) : No contact but contact possible with a neighbouring segment |
|Q(5)|VR: Relative sliding speed |
|Q(6)|VS: Relative sliding speed |