1. Thermo-mechanics J. Cugnoni, LMAF / EPFL 2009

2. Three kind of « thermo-mechanics » 1. Un-coupled: Known temperature field => mechanical model (linear statics + th. expansion) 2. One way coupling: solve thermal problem => temperature field => solve mechanical problem 3. Fully coupled: solve at the same time temperature & displacement field (includes mechanical dissipation)

3. Thermal problem Variables  Essential variable: Temperature field T  Natural variable: heat flux q Material  Conductivity  Density  & specific heat c p if transient Boundary conditions:  Temperature: T surf = f(t) if transient  Surface heat fluxes: Imposed heat flux q surf =f(t) Convection: q surf = h (T –T ext (t))  Volume heat source: s = f(t) T,, , cp, s q T ext

4. 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 Loading:  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 T ext  If transient: define an amplitude curve (tool => amplitude), need to start at zero for t=0,

5. 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 Loading:  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 T ext  If transient: define an amplitude curve (tool => amplitude), need to start at zero for t=0

6. 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

7. Demo: thermal switch Beam dimensions 60 x 5 x 1 mm Steel, 0.5 mm Invar, 0.5 mm Prop.SteelInvar Young’s modulus 210 GPa141 GPa Poisson ratio0.3 Th. Expansion1 e -51 e -6 Density7800 kg/m38000 kg/m3 Conductivity30 W/m/K10 W/m/K Specific heat1000 J/kg/K500 J/kg/K Time (s) 160 T=100°C T=0°C Water Convection: q=h (T-Text), h = 100 W/m2/K T water = f(time) Block: clamped, T= 0°C