# Thermo-mechanics

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```					Thermo-mechanics

J. Cugnoni, LMAF / EPFL 2009
Three kind of « thermo-mechanics »
1.    Un-coupled: Known temperature field => mechanical
model (linear statics + th. expansion)
  u   el   th ;  th   T ;   C  el  C (u  T )
  (C (u  T ))  f  0
2.    One way coupling: solve thermal problem =>
temperature field => solve mechanical problem
T
 cp       ( T )  s    (C (u  T ))  f  0
t
3.    Fully coupled: solve at the same time temperature &
displacement field (includes mechanical dissipation)
        T
 c p          ( T )  s  0
        t
   (C (u  T ))  f  0

Thermal problem
   Variables
   Essential variable: Temperature field T              q
   Natural variable: heat flux q

   Material                                        Text
   Conductivity 
   Density  & specific heat cp if transient
T, , , cp, s
   Boundary conditions:
   Temperature: Tsurf = f(t) if transient
   Surface heat fluxes:
   Imposed heat flux qsurf=f(t)
   Convection: qsurf = h (T –Text(t))
   Volume heat source: s = f(t)
Thermal problem in Abaqus
   Select Step = Heat transfer
   Choose steady state or transient
   If transient: set time period, set small initial increment, set max
T per increment (<1/10 of max T)
   In Mesh:
   select element type: Heat transfer, linear
   Need to impose at least one temp. (rigid body)
   Adiabatic interface: leave free = no flux!
   Flux = load, Temperature = BC
   Convection: in interaction module, create Surface Film condition,
enter h and Text
   If transient: define an amplitude curve (tool => amplitude), need
to start at zero for t=0,
Coupled Thermo mechanics in Abaqus

   Select Step = Coupled Temp-Displacement
   Choose steady state or transient
   If transient: set time period, set small initial increment, set max
T per increment (<1/10 of max T)
   In Mesh:
   select element type: Coupled Temp.-Displacement, quadratic
   Need to impose at least one temp. & block 6 rigid body motions
   Adiabatic interface: leave free = no flux!
   Flux = load, Temperature = BC
   Convection: in interaction module, create Surface Film condition,
enter h and Text
   If transient: define an amplitude curve (tool => amplitude), need
to start at zero for t=0
Démos
   Bi-material beam: Thermal switch
 Coupled  Thermo-mechanical problem
 Transient analysis
 Heat transfer & expansion properties
 Heat transfer BC:
   Temperature
   Convection
   Heat Flux
   Time dependent boundary conditions
Demo: thermal switch
Block: clamped, T= 0°C

Beam dimensions 60 x 5 x 1 mm

Invar, 0.5 mm

Water

Prop.                         Steel         Invar                                      Steel, 0.5 mm
Young’s                       210 GPa       141 GPa
modulus                                                           T water = f(time)
Poisson ratio                 0.3           0.3                                       T=100°C
Th. Expansion                 1e-5          1e-6

Density                       7800 kg/m3    8000 kg/m3

Conductivity                  30 W/m/K      10 W/m/K

Specific heat                 1000 J/kg/K   500 J/kg/K
T=0°C
1           Time (s)         60

```
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 views: 10 posted: 10/13/2011 language: English pages: 7