/THERM_STRESS/MAT
Block Format Keyword Used to add thermal expansion property for Radioss material (shell and solid).
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/THERM_STRESS/MAT/mat_ID  
fct_ID_{T}  Fscale_{y} 
Definitions
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) 
$\left[\frac{1}{\text{K}}\right]$ 
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 

4nodes shells: only
for BelytshkoTsai and QEPH elements (I_{shell} =1, 2, 3, 4 and 24) 3nodes shells: only for standard triangle (I_{sh3n} =1, 2) 
✓ 
✓ = yes
blank = no
Example (Thermal)
#RADIOSS STARTER
#12345678910
# 1. MATERIALS:
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
/MAT/PLAS_JOHNS/1/1
Steel
# RHO_I
7.8E9 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 IFORM
273 3.588 19.0 0 1
# Blank card
/THERM_STRESS/MAT/1/1
# func_IDT Fscale_y
1003 0
#12345678910
# 2. FUNCTIONS:
#12345678910
/FUNCT/1003
linear expansion coefficient funtion of temperature
# X Y
273 1.2E5
800 1.2E5
#12345678910
#enddata
#12345678910
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) $$\langle {\epsilon}_{\mathit{th}}\rangle =\langle \alpha \Delta T\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\alpha \Delta T\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\alpha \Delta T0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0\rangle $$Where, α is the isotropic thermal expansion coefficient.
$\text{\Delta}T=T{T}_{ref}$ 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) $$\epsilon ={\epsilon}_{th}+{\epsilon}_{meca}$$This change in temperature causes stress. The thermal stress can be calculated from Hook's law.(3) $${\mathbf{\sigma}}_{\mathit{th}}=H{\mathbf{\epsilon}}_{th}$$Where, H is the elasticity matrix.
It is important to define boundary conditions with particular care for problems involving thermal loading to avoid overconstraining 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.