====== LLIEN ======
===== Description =====
Penalty law for shell/solids link element [[elements:lien3|LIEN3]]

==== The model ====
This law is only used for mechanical analysis of shell models, using shell elements linked to solid elements with the link element [[elements:lien3|LIEN3]].
==== Files ====
Prepro: LLIEN.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| = 33 |
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
None

==== Real parameters ====
^Line 1 (1G10.0)^^
|RIGK|	Penalty coefficient $K$ (link-spring stiffness)|
===== Stresses =====
==== Number of stresses ====
1
==== Meaning ====
|SIG(1)| = Mean elongation of the different springs used in LIEN3 link element|
\[
= \frac{1}{N+1} \sum_{k=0}^N \sqrt{\Delta X_k^2 + \Delta Y_k^2 + \Delta Z_k^2}
\]

===== State variables =====
==== Number of state variables ====
3
==== List of state variables ====
|Q(1)| $n_1$|
|Q(2)| $n_2$ director vector components.|
|Q(3)| $n_3$|