/THERM_STRESS/MAT

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/THERM_STRESS/MAT/`mat_ID`
`fct_ID`_T	`Fscale`_y

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`fct_ID`_T	Function identifier for defining the instantaneous thermal linear expansion coefficient as a function of temperature. (Integer)
`Fscale`_y	Ordinate scale factor for thermal expansion coefficient function. Default = 1.0 (Real)	$[\frac{1}{K}]$ $[\frac{1}{K}]$

Element Compatibility - Part 1

2D Quad	8 node Brick	20 node Brick	4 node Tetra	10 node Tetra	8 node Thick Shell	16 node Thick Shell
✓	✓	✓	✓	✓	✓	✓

✓ = yes

blank = no

Element Compatibility - Part 2

SHELL	TRUSS	BEAM
4-nodes shells: only for Belytshko-Tsai and QEPH elements (`I`_shell =1, 2, 3, 4 and 24) 3-nodes shells: only for standard triangle (`I`_sh3n =1, 2)		✓

✓ = yes

blank = no

▸Example (Thermal)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/PLAS_JOHNS/1/1
Steel 
#              RHO_I
              7.8E-9                   0
#                  E                  Nu
              210000                  .3
#                  a                   b                   n           EPS_p_max            SIG_max0
                 270                 450                  .6                   0                   0
#                  c           EPS_DOT_0       ICC   Fsmooth               F_cut               Chard
                   0                   0         0         0                   0                   0
#                  m              T_melt              rhoC_p                 T_r
                   0                   0                   0                   0
/HEAT/MAT/1/1
#                 T0             RHO0_CP                  AS                  BS     
                 273               3.588                19.0                   0         
# Blank card

/THERM_STRESS/MAT/1/1
# func_IDT            Fscale_y
      1003                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1003
linear expansion coefficient funtion of temperature
#                  X                   Y
                 273              1.2E-5                                                            
                 800              1.2E-5                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

The /THERM_STRESS/MAT option should be used with thermal material. This option is not compatible with ALE applications (/ALE, /EULER). There is no thermal coupling between an ALE thermal material and a Lagrangian thermal material. /HEAT/MAT should be defined for thermal analysis and temperature change computation.
For shells this option is available with all material laws.
For solids this option is available only for material laws where the number goes from 1 to 28 and laws number 36, 42, 44, 45, 46, 47, 48, 49, 50, 56, 60, 62, 65, 66, 68, 69, 72, 74, 79, 81, 82, 88, 92, 103, 106.
This option is not available for implicit analysis.
The thermal expansion generates thermal strains which are defined as:(1)
$⟨ ε_{th} ⟩ = ⟨ α Δ T α Δ T α Δ T 000 ⟩$ $〈 ε_{th} 〉 = 〈 α Δ T α Δ T α Δ T 0 0 0 〉$

Where, α is the isotropic thermal expansion coefficient.

$Δ T = T - T_{r e f}$ $Δ T = T - T_{r e f}$ is the temperature gradient or temperature increment between current time and reference.

The total strain is considered as the sum of subsequently mechanical and thermal effect:(2)
$ε = ε_{t h} + ε_{m e c a}$ $ε = ε_{t h} + ε_{m e c a}$

This change in temperature causes stress. The thermal stress can be calculated from Hook's law.(3)
$σ_{th} = H ε_{t h}$ $σ_{th} = H ε_{t h}$

Where, H is the elasticity matrix.

It is important to define boundary conditions with particular care for problems involving thermal loading to avoid over-constraining the thermal expansion. Constrained thermal expansion can cause significant stress, and it introduces strain energy that will result in an equivalent increase in the total energy of the model.