/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_IDT Fscaley

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)
fct_IDT Function identifier for defining the instantaneous thermal linear expansion coefficient as a function of temperature.

(Integer)
Fscaley Ordinate scale factor for thermal expansion coefficient function.

Default = 1.0 (Real)

 [ 1 K ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaaigdaaeaacaWGlbaaaaGaay5waiaaw2faaaaa@3981@

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

(Ishell =1, 2, 3, 4 and 24) 3-nodes shells: only for standard triangle (Ish3n =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

  1. 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.
  2. This option is available for all material laws; except for the following:

    LAW0, 5, 6, 11, 21, 26, 37, 41, 46, 51, 54, 97, 108, 113, 151, /MAT/B-K-EPS, /MAT/K-EPS, and /MAT/GAS

  3. This option is compatible with equations of state, /EOS, only when used with the following materials: LAW3, 4, 12, and 49
  4. This option is not available for implicit analysis.
  5. The thermal expansion generates thermal strains which are defined as:
    〈 ε th 〉 = 〈 α Δ T           α Δ T         α Δ T 0         0         0 〉

    Where, α MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@ is the isotropic thermal expansion coefficient.

    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:

    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.

    σ th = H ε t h

    Where, H MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaaaa@36C0@ 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.