# Material constitutive laws

• In the links below you will find the documentation concerning the different constitutive laws implemented in SMART+ :

# Elastic Laws

### umat_elasticity_iso(vec, vec, vec , mat, mat , int, double, int, double , double, double, double, double , double , double, int, int, bool)

Code name : ELISO
This is a user subroutine for isotropic elastic materials in 1D to 3D case in order to solve thermo-elastic problem. This Umat calls only the classical variables, please see the documentation about Umat for more informations.

The isotropic elasticity Umat requires three material constants write in the material.dat file :

E = props : Young Modulus
$$\nu$$= props  : Poisson ratio
$$\alpha$$= props  : coefficient of thermal expansion

Then various formulas will be used considering the problems dimensions. Please see the constitutive laws part in the theory manual for more informations about constitutive laws.

Example of material.dat file :

Material
Name	ELISO
Number_of_material_parameters 3
Number_of_internal_variables 0

E 200000
nu 0.3
alpha 17.E-6


### umat_elasticity_trans_iso(vec, vec, vec , mat, mat , int, double, int, double , double, double, double, double , double , double, int, int, bool)

Code name : ELIST
This is a user subroutine for transversaly isotropic elastic materials in 1D to 3D case in order to solve thermo-elastic problem. This Umat calls only the classical variables, please see the documentation about Umat for more informations

The transversaly isotropic elasticity Umat requires eight material constants write in the material.dat file:

axis = props : Axis of transverse isotropy (1 to 3)
EL = props : Axial Young Modulus
ET = props : Transverse Young Modulus
$$\nu$$ TL = props : Axial Poisson ratio
$$\nu$$ TT = props : Transverse Poisson ratio
GLT = props : Axial shear modulus
$$\alpha$$ L = props : Axial coefficient of thermal expansion
$$\alpha$$ T = props : Transverse coefficient of thermal expansion

Then various formulas will be used considering the problems dimensions. Please see the constitutive laws part in the theory manual for more informations about constitutive laws.

Example of material.dat file :

Material
Name	ELIST
Number_of_material_parameters 8
Number_of_internal_variables 0

axis 1
EL 278
ET 22
nuTL 0.10
nuTT 0.38
GLT 20
alphaL 17.E-6
alphaT 17.E-6