====== RESS ======

===== Description =====


The RESS formulation employs just the Enhanced Assumed Strain (EAS) technique with a reduced integration scheme. 
{{ :elements:blz3d.png?300|}} These elements have special integration schemes dedicated to analyze problems involving non-linear through-thickness distribution without requiring many element layers. \\

Implemented by: J.I. Velosa de Sena, December 2010

Type: 69

Prepro: RESS3A.F \\
Lagamine: RESS3B.F\\

===== Input file =====
^Title (A5)^^
|TITLE  | 'RESS3' en colonnes 1 à 5|
^Control data (4I5)^^
|NELEM|Number of elements|
|NEAS|Number of EAS modes (Enhanced Assumed Strain) - only available value = 1|
|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|
|NPTH|Number of integration points on the width (in the ζ direction) of the element (NPTH ∈ [2,10]). The number of integration points in the ξ-η plane is equal to 4.|
^List of EAS modes (14I5)^^
|EAS(1)|if NEAS = 1|
^Definition of the elements (I5/8I5)^^ 
|LMATE|Material law|
|NODES(8)|List of nodes|
===== Results =====
Cauchy stresses in global axes $\sigma_x,\sigma_y,\sigma_z,\sigma_{xy},\sigma_{xz},\sigma_{yz}$

===== Order of the integration points =====
Starting from negative coordinates, one varies: \\
  - the ξ
  - the η
  - the ζ
__Exemple for 3 IP (NPTH=3)__ \\ 
  - ξ = 0 η = 0 ζ = -0.774 
  - ξ = 0 η = 0 ζ = 0 
  - ξ = 0 η = 0 ζ = +0.774