Lagamine

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====== ELATH ======

===== Description =====

Elastic constitutive law with thermal effects for solid elements at variable temperature.

==== The model ====

This law is used for a coupled thermo-mechanical analysis of elastic solids undergoing large strains.

==== Files ====

Prepro: LELATH.F \\
Lagamine: 
  * ELAC2S.F (Plane stress state);
  * ELAC2E.F (Plane strain state);
  * ELAC2A.F (Axisymmetric state);
  * ELA2CG.F (Generalized plane state).

===== Availability =====

|Plane stress state| YES |
|Plane strain state| YES |
|Axisymmetric state| YES|
|3D state| NO |
|Generalized plane state| YES |

===== Input file =====


==== Parameters defining the type of constitutive law ====

^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 200|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|

==== Integer parameters ====

^ Line 1 (2I5) ^^
|NTEMP| number of temperatures at which material data are given|
|IENTH| = 1 to use the enthalpy formulation of the heat problem |
|:::| = 0 to use the classical formulation of the heat problem |

==== Real parameters ====

Repeat NTEMP times the definition of those parameters. \\

^ Line 1 (4G10.0) ^^
|T| Temperature |
|E| YOUNG's elastic modulus at temperature T |
|ANU| POISSON's ratio at temperature T |
|ALPHA| thermal expansion coefficient at temperature T |

Note that these values are tangent values (and not secant values). \\

^ Line 2 (1G10.0) ^^
|RHO| Specific mass (used to take into account self-weight but only if the initial specific mass is constant) |

===== Stresses =====

==== Number of stresses ====

6 for 3D state \\ 4 for the other cases

==== Meaning ====

The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates. \\
For the 3-D state:
|SIG(1)|$\sigma_{xx}$|
|SIG(2)|$\sigma_{yy}$|
|SIG(3)|$\sigma_{zz}$|
|SIG(4)|$\sigma_{xy}$|
|SIG(5)|$\sigma_{xz}$|
|SIG(6)|$\sigma_{yz}$|
For the other cases:
|SIG(1)|$\sigma_{xx}$|
|SIG(2)|$\sigma_{yy}$|
|SIG(3)|$\sigma_{xy}$|
|SIG(4)|$\sigma_{zz}$|

===== State variables =====

==== Number of state variables ====

1

==== List of state variables ====

|Q(1)|Element thickness (t) in plane stress state|
|:::| = 1 in plane strain state |
|:::| Circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetric state |
|:::| = 0 in 3-D state |
|:::| element thickness (t) in generalized plane state |
Lagamine

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