====== MESO2 ======
DELETEME This law does not seem to exist in the code. \\
LMESO2.F does not exist. \\
ITYPE = 295 corresponds to law [[laws:fczm|FCZM]]
===== Description =====
Elastic visco-plastic constitutive law for solidification problem (continuous casting) (always used with [[laws:thsol2|THSOL2]])
==== The model ====
For liquid element: ferrostatic pression\\ For solid  element: EVP-law (see [[laws:grob|GROB]]) \\ For mushy  element: EVP-law with parameters interpolated between solid and liquid state
==== Files ====
Prepro: LMESO2.F \\
===== Availability =====
|Plane stress state|NO|
|Plane strain state|NO|
|Axisymmetric state|YES |
|3D state|NO|
|Generalized plane state|NO|
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 295|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing.|
==== Integer parameters ====
^ Line 1 (3I5) ^^
|NINTV|number of sub-steps used to integrate numerically the constitutive equation in time-step|
|METK|0 analytical stiffness matrix \\ 1 stiffness matrix computed by perturbation|
|ISOL|0 use of total stresses in the constitutive law\\ 1 use of effective stresses in the constitutive law|
==== Real parameters ====
^Line 1 (3G10.0)^^
|COOY|level of liquid surface|
|TS|temperatures (see [[laws:thsol2|THSOL2]])|
|TL|:::|
^Line 2 (7G10.0)^^
|EO|reference YOUNG's elastic modulus ($E_o$)|
|BE|corresponding temperature coefficient ($b_E$)|
|ANUO|reference POISSON's ratio ($\nu_0$)|
|BNU|corresponding temperature coefficient ($b_\nu$)|
|ANO|reference strain rate exponent ($n_o$)\\ let us recall that: \\ E=$E_o$exp($-b_o T$)\\ $\nu = \nu_o exp(\nu_K T$), where T is the absolute temperature (K)|
|BO|reference strain rate coefficient ($B_o$)|
|Q|corresponding temperature coefficient (Q)|
^Line 3 (7G10.0)^^
|AMO|reference hardening exponent ($m_o$)|
|AKSO|reference hardening saturation coefficient ($K_{so}$)|
|GAMMAO|reference hardening parameter ($\gamma_o$)|
|TETAO|reference hardening coefficient ($\theta_o$)|
|BTETA|corresponding temperature coefficient ($b_\theta$)|
|AKOO|reference initial yield limit ($K_{oo}$) |
|BK|corresponding temperature coefficient ($b_K$)|
^Line 4 (2G10.0)^^
|RGA2|perfect GAZ constant in correct unity system|
|CTQ|TAYLOR QUINNEY coefficient\\  0 for solidification case \\ < 0 for semi-coupled thermomechanical analysis when the $\sigma(8)$ has to be constant and null CTQ has to be used|

==== Number of stresses ====
4
==== Meaning ====
|SIG(1)| $\sigma_{11}$|
|SIG(2)| $\sigma_{22}$ |
|SIG(3)| $\sigma_{12}$|
|SIG(4)| $\sigma_{33}$|
===== State variables =====
==== Number of state variables ====
3
==== List of state variables ====
|Q(1)|THICK|
|Q(2)| current yield limit in tension, its initial value is  $K_o$ exp (-$b_K$ T), where T is the absolute temperature (K) |
|Q(3)| $\varepsilon^{P}$ equivalent nonlinear strain|