====== BINDS ======
===== Description =====
Constitutive law for [[elements:binds|BINDS]] elements.

==== The model ====
This law is used to enforce non-linear constraints between several degrees of freedom of the discretized structure.
==== Files ====
Prepro: LBINDS.F \\

===== Availability =====
|Plane stress state| YES |
|Plane strain state| YES|
|Axisymmetric state| YES |
|3D state| YES|
|Generalized plane state| YES|
===== Input file =====

==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 30|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (5I5) ^^
|LTYP1| = 1 to enforce elastic constraints \\ = 2 to enforce elasto-plastic constraints \\ = 3 to enforce bi-linear elastic constraints|
|NALPHA| number of different α<sub>i</sub> coefficients in the constraint equation (including α<sub>0</sub>)|
|ICODE| = 0 if the constraint equation enforces a rigid body mode \\ = 1 else|
|NDEF| Number of times of definition for α sets|
|IBEND |= 0 generally \\ = 1 if management of bending/unbending thanks to generalized plane strain state|
==== Real parameters ====
=== 1. LTYP1 = 1 ===

^ Line 1 (7G10.0) - repeated as many times as necessary ^^
|ALPHA(I) \\ I = 1,NALPHA| The α<sub>i</sub> coefficients of the constraint equation|
^Line n=round(NALPHA/7) (G10.0)^^
|TRACE|K<sub>1</sub> = the elastic stiffness of the constraint |
=== 2. LTYP1 = 2 ===
^ Line 1 (7G10.0) - repeated as many times as necessary ^^
|ALPHA(I) \\ I = 1,NALPHA| The α<sub>i</sub> coefficients of the constraint equation|
^Line n=round(NALPHA/7) (3G10.0)^^
|TRACE(1)|K<sub>1</sub> = the elastic stiffness of the constraint |
|TRACE(2)|K<sub>2</sub> = the tangent elasto-plastic stiffness of the constraint|
|LH1|The elastic limit of the constraint|
=== 3. LTYP1 = 3 ===
^ Line 1 (7G10.0) - repeated as many times as necessary ^^
|ALPHA(I) \\ I = 1,NALPHA| The α<sub>i</sub> coefficients of the constraint equation|
^Line n=round(NALPHA/7) (2G10.0)^^
|TRACE(1)|K<sub>1</sub> = the elastic stiffness in tension |
|TRACE(2)|K<sub>2</sub> = the elastic stiffness in compression|

==== Remarks ====
  - if IBEND = 0 : coefficient α<sub>0</sub> is multiplied by DMULT during the simulation
  - if IBEND = 1 : in generalised plane strain state, thickness is given by: e(x,y) = A + B.x + C.y \\ α<sub>1</sub> is the coefficient of “A” and it must be equal to the curve in the OXZ plane \\ α<sub>2</sub> is the coefficient of “B” and it must be equal to 1.0 \\ α<sub>0</sub> is automatically computed

===== Stresses =====
==== Number of stresses ====
1
==== Meaning ====
|SIG(1)|The generalized force necessary to enforce the constraint.|

===== State variables =====
==== Number of state variables ====
  * 1 if LTYP = 1
  * 2 if LTYP = 2
  * 1 if LTYP = 3
==== List of state variables ====
=== 1. LTYP1 = 1 (elastic constraint) ===
|Q(1)| = 0 (meaningless)|
|Q(6)| = strain energy|
=== 2. LTYP1 = 2 (elasto-plastic constraint) ===
|Q(1)|current yield limit ; its initial value is LH1|
|Q(2) |= 0 if the current state is elastic \\ = 1 if the current state is elasto-plastic.|
|Q(6)| strain energy|
=== 3. LTYP1 = 3 (bi-linear elastic constraint) ===
|Q(1)| = 0 if the current state is in tension \\ = 1 if the current state is in compression|