====== ARBTHMET ======
===== Description =====
Elasto-plastic constitutive law coupled with thermal and metallurgical effects in solids
==== The model ====
This law is only  used for coupled thermal, metallurgical, mechanical analysis of solids submitted to heat flow, metallurgical phase changes and mechanical stresses and strains.
==== Files ====
Prepro: LARBTM.F \\
===== Availability =====
|Plane stress state| NO |
|Plane strain state| NO |
|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| 350 |
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (I5) ^^
|NINTV| = number of sub-steps used to integrate numerically the constitutive equation in a time step. |
==== Real parameters ====
^ Line 1 (2G10.0 ) ^^
|RE| initial yield limit ($=R_{eo}$) |
|ET| initial élastomère-plastic tangent modules ($=E_{to}$) |
These data are to be given at the initial temperature and for the initial metallurgical composition of the solid. The other data are stored on a data file available to the pre‑processor. The description of this file is with the law [[laws:metamec|METAMEC]].
===== Stresses =====
==== Number of stresses ====
= 6 for the 3-D 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 analysis :
|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 2D analysis :
|SIG(1)|$\sigma_{xx}$|
|SIG(2)|$\sigma_{yy}$|
|SIG(3)|$\sigma_{xy}$|
|SIG(4)|$\sigma_{zz}$|

===== State variables =====
==== Number of state variables ====
6
==== 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|
|Q(2)|current yield limit in tension, its initial value is $=R_{eo}$ |
|Q(3)| = 0 if the current state is elastic |
|:::| = 1 if the current state is elasto‑plastic|
|Q(4)|equivalent plastic strain due to mechanical effects ($\bar{\varepsilon}^p$) |
|Q(5)|equivalent plastic strain due to phase transformations ($\bar{\varepsilon}^{ph}$) |
|Q(6)|current value of the elasto‑plastic tangent modulus; its initial value is $=E_{to}$ |