Lagamine

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====== CNTSH ======

===== Description =====

Constitutive law for unilateral contact with friction for:
  * Plane membrane elements ([[elements:mem2d|MEM2D]]);
  * Thin plane shell elements ([[elements:kirsh|KIRSH]]);
  * Thick plane shell elements ([[elements:minds|MINDS]]).

==== The model ====

This law is used for mechanical analysis of unilateral contact with friction in generalized plane state for shells and membranes.\\

Contact can occur on both sides of shell (or membrane).\\

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

COULOMB behaviour is assumed, with variable friction coefficient.

==== Files ====

Prepro: LCNTSH.F \\
Lagamine: CNTSH.F

===== Availability =====

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

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

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

^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 91|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|

==== Integer parameters ====

^ Line 1 (I5) ^^
|N| Number of points defining the COULOMB behaviour |
|:::| Shear stress ($\tau$) vs Pressure (p) |

Remark :
  * N must be equal to 2 or greater ;
  * The constitutive law will be stored in central memory. So we must have the following condition : \[2\times N + 2 \leq MPARA\]

==== Real parameters ====

=== Global datas ===

^ Line 1 (2G10.0) ^^
|RIGP| Penalty coefficient on pressure ($K_p$) |
|RIGT| Penalty coefficient on shear ($K_{\theta}$) (default = RIGP) |

=== COULOMB constitutive law ===

To repeat N times :
^ Line 1 (2G10.0) ^^
|P| Pressure p of the considered point |
|T| Shear z of the considered point |

Warning: The first point must always be taken at p=0.

===== Stresses =====

==== Number of stresses ====

2

==== Meaning ====

|SIG(1)| = p : Pressure |
|:::| > 0 in compression |
|SIG(2)| = $\tau$ : Shear |
|:::| > 0 according with $\xi$ coordinate of shell (membrane) |

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

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

7

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

|Q(1)|ISEG: Number of foundation segment in contact |
|Q(2)|TO: Side of the shell in contact |
|Q(3)|WT: Total work associated to the integration point (by unit of shell area) |
|Q(4)|WD: Dissipated work associated to the integration point (by unit of shell area) |
|Q(5)|D: Penetration d (positive if contact occur) |
|Q(6)|V: Sliding speed (positive with $\xi$ coordinate of shell) |
|Q(7)|TC: Maximum shear stress, according to the COULOMB constitutive law and the pressure |
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