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====== BRILS ======
Volumic element
===== Description =====
{{  :elements:3delem.png?600  |}}
Type: 21 \\
Implemented by: AM Habraken, 1982 \\
==== Files ====
Prepro: BRILSA.F \\
Lagamine: BRILSB.F
===== Input file =====
^Title (A5)^^
|TITLE|"BRILS" in the first 5 columns|
^Control data (4I5)^^
|NELEM|Number of elements|
|ISPMAS| = 0 Nothing \\ = 1 Take into account specific mass if NTANA = -1|
|INSIG| = 0 No initial stresses \\ = 1 Initial stresses |
|ILOAX| = 0 Use of global axes|
^Specific mass for dynamic analysis - Only if ISPMAS = 1 (G10.0)^^
|SPEMAS|Specific mass|
^Initial stresses - Only if INSIG ≠ 1^^
|If INSIG = 1 → $\sigma_Z=\sigma_{Z0}+zd\sigma_z$ \\ If INSIG = 2 → $\sigma_Z = \min(\sigma_{Z0}+zd\sigma_z, \phi*D\phi)$ ||
|SIGZ0|$\sigma_{Z0}$ effective stress $\sigma_Z$ at the axis origin|
|DSIGZ|Gradient of effective stress along Z axis|
|AK0|$k_0$ ratio $\sigma_x/\sigma_z$ ($=\sigma_y/\sigma_z$)|
|In the case where this element is used for an analysis in effective stress (cf ISOL parameter in the constitutive law), on needs: \\  - To define a pressure $p$ through the DoF n°4 \\  - Fix this DoF in the FIXED section of the *.lag file \\  - Use control parameter NTANA = 4 \\ The computation of SIGZ0 and DSIGZ must then be performed from effective stresses, from which the water pressure is substracted: $\sigma'=\sigma - p$||
^Element definition (5I5/14I5/14I5)^^
|NNODE|Number of node of the element: 8, 16, 20, 24, or 32|
|NPI(1)|Number of integration points in each direction|
|NPI(2)|:::|
|NPI(3)|:::|
|LMATE|Material law|
|NODE(NNODE)|List of nodes|
===== Results =====
Cauchy stresses in global axes $\sigma_x,\sigma_y,\sigma_z,\sigma_{xy},\sigma_{xz},\sigma_{yz}$

===== Notes =====
**Order of the integration points** \\
Starting from negative coordinates, one varies: \\
  - the ξ
  - the η
  - the ζ
Example for 8 IP:
  - ξ = -0,57; η = -0,57; ζ = -0,57
  - ξ = -0,57; η = -0,57; ζ = +0,57
  - ξ = -0,57; η = +0,57; ζ = -0,57
  - ξ = -0,57; η = +0,57; ζ = +0,57
  - ξ = +0,57; η = -0,57; ζ = -0,57
  - ξ = +0,57; η = -0,57; ζ = +0,57
  - ξ = +0,57; η = +0,57; ζ = -0,57
  - ξ = +0,57; η = +0,57; ζ = +0,57


**Non classic bricks** \\
The 32 node brick can be complete like the one shown in the figure, but it can also have null intermediary nodes meaning the corresponding edge is linear or parabolic. In that case, the list of nodes still contains 8 non-zero vertex nodes, then the intermediary nodes ordered as presented in the figure, with some equal to zero. \\ This brick can therefore be degenerated to obtain the other types of bricks or any type of bricks.Thus, it can be used for a smooth transition from a refined mesh with 32-nodes bricks to a coarser mesh with 8-node bricks, without using triangular bricks. \\ Be careful, one must use a number of integration points in each direction that corresponds to the degree of the displacement field in that direction. \\ This brick can be used to tend towards triangular bricks, in which case the degenerated edge must be linear. For other bricks, a null node is not accepted.
Lagamine

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