====== BLZ3D/BWD3D ======

===== Description =====

{{ :elements:blz3d.png?300|}}
8 node large strain volumetric element with hourglass and locking control. \\

Implemented by: Zhu Yongyi, January 1992 \\
Improved by: Laurent Duchêne and Pierre de Montleau, August 2004 (BWD3D version)

Type: 22

Prepro: BLZ3DA.F \\
Lagamine: BLZ3DB.F, BWD3DB.F\\

===== Input file =====
^TITLE (A5)^^
|TITLE  | 'BLZ3D' in columns 1 to 5|
^CONTROL (5I5)^^
|NELEM  | Number of elements |  
|INDPP  |= 0 if no weight (or no density if NTANA=-1)|
|:::    |= 1 if weight taken into account (or density)|
|INSHE  |= 0 for automatic calculation of shear locking parameter|
|:::    |= 1 if shear coefficient taken into account (see below)|
|:::    |= -1 for use of element BWD3D (only 1 integration point)|
|ILOAX  |= 0 for global axis computation \\ ☛ Objectivity must be verified in the material law (with Jaumann correction)\\ ☛ No rotation of material axes|
|:::|< 0 for computation with constant and symetrical velocity gradients \\ pseudo local axes : use of local axes on the time step but no evolution of the local axes on the following time step \\ ☛ Objectivity is verified \\ ☛ No rotation of material axes|
|:::|> 0 for computation with local axes \\ ☛ Objectivity is verified \\ ☛ Rotation of material axes|
|:::|units: \\ = 1 for rotations incorporated in local tangent matrix :!: **Not available** \\ = 2 apply final rotation to local tangent matrix \\ = 3 apply initial rotation to local tangent matrix \\ = 4 compute tangent matrix through global perturbation method|
|:::|tens (only for ILOAX>0): \\ = 0 for local axes e<sub>1</sub>, e<sub>2</sub>, e<sub>3</sub> initially parallel to global axes e<sub>x</sub>, e<sub>y</sub>, e<sub>z</sub> \\ = 1 for local axes e<sub>1</sub>, e<sub>2</sub>  given (and e<sub>3</sub>=e<sub>1</sub>∧e<sub>2</sub>) \\ = 2 for local axes e<sub>1</sub>, e<sub>2</sub>  initially in the plane (e<sub>x</sub>, e<sub>y</sub>) forming an angle θ with e<sub>x</sub>, e<sub>y</sub> (and e<sub>3</sub>=e<sub>1</sub>∧e<sub>2</sub>)\\ = 3 same as 1 with different local axes for each element \\ = 4 same as 2 with different local axes for each element|
|ISIG0| = 0 if no initial stresses|
|:::| = 1 for input of initial stresses|
^CONSIDERATION OF WEIGHT (4G10.0) \\ Only if INDPP = 1 ^^
|WSPE(1)| = specific weight in X direction|
|WSPE(2)| = specific weight in Y direction|
|WSPE(3)| = specific weight in Z direction|
|WSPE(4)| = density| 
^CONSIDERATION OF SHEAR LOCKING (1G10.0) \\ Only if INSHE = 1 ^^
|PARSHE| Shear locking coefficient ∈ [0,1] \\ - close to 0: avoid shear locking but higher risk of hourglass modes (use for thin elements in flexion) \\ - close to 1: avoid hourglass modes but higher risk of shear locking (use for cubic elements in shear)|
^INITIAL ORIENTATION OF LOCAL AXES (6G10.0) \\ Only if tens of ILOAX = 1 or 3 \\ (only one line if tens of ILOAX = 1, repeated for each element if tens of ILOAX = 3) ^^
|e<sub>1</sub>(x)|coordinate of e<sub>1</sub> along e<sub>x</sub>|
|e<sub>1</sub>(y)|coordinate of e<sub>1</sub> along e<sub>y</sub>|
|e<sub>1</sub>(z)|coordinate of e<sub>1</sub> along e<sub>z</sub>|
|e<sub>2</sub>(x)|coordinate of e<sub>2</sub> along e<sub>x</sub>|
|e<sub>2</sub>(y)|coordinate of e<sub>2</sub> along e<sub>y</sub>|
|e<sub>2</sub>(z)|coordinate of e<sub>2</sub> along e<sub>z</sub>|
|Note: These vectors are normalized after reading but should be orthogonal: \\ e<sub>1</sub> • e<sub>2</sub> = e<sub>1</sub>(x) * e<sub>2</sub>(x) + e<sub>1</sub>(y) * e<sub>2</sub>(y) + e<sub>1</sub>(z) * e<sub>2</sub>(z) = 0||
^INITIAL ORIENTATION OF LOCAL AXES (1G10.0) \\ Only if tens of ILOAX = 2 or 4  \\ (only one line if tens of ILOAX = 2, repeated for each element if tens of ILOAX = 4)^^
|THETA| Angle between e<sub>1</sub> and e<sub>x</sub> in degrees|
^DEFINITION OF THE ELEMENTS (2I5/8I5/6G10)^^
|NINTE| Number of integration points (1, 2, 4 or 8) \\ if NINTE = 1, add 40 to MVARI compared to maximum required by laws |
|LMATE| Number of the material law|
|NODES(8)| List of nodes|
|SIG0(6)| List of initial stresses (Only if ISIG0=1)|