Example1 Deformation of Conductive Strip due to Heating

General

Voltage is applied across a conductive strip line. The current going through the strip line is solved.
Then the eventual joule loss and temperature rise are solved.
By performing mechanical stress analysis, the deformation due to the temperature rise is examined.
The steady-state analysis is performed for the model on Exercise 2 of electric field-thermal coupled analysis. The results are handed over to mechanical stress analysis.
Unless specified in the list below, the default conditions will be applied.

Analysis Space

Item	Settings
Analysis Space	3D
Model unit	mm

Analysis Conditions

Solvers used are Curie and Galileo.

Item	Settings
Solver	Electric field – thermal coupled analysis [Curie} Mechanical stress analysis [Galileo]
Analysis Type (Curie)	Steady-state analysis
Options	N/A *

* “Thermal Load” is selected by default for the thermal load-mechanical stress coupled analysis.

The reference temperature is set on the Step/Thermal Load tab.

Tabs	Setting Item	Settings
Step/Thermal load	Reference temperature	25[deg]

* The reached temperatures come from the thermal analysis.

Model

The same as Exercise 2 of electric field-thermal coupled analysis.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	Board	001_Alumina *
6/Solid	Strip	008_Cu *

* Available from the Material DB

It is assumed that there is no current flow in the alumina substrate.

Body Attribute Name	Thickness/Width	Analysis Domain
Board		Usable Domains: Deselect “For use in electric field analysis”

Resistivity needs to be set for Board for [Curie] even though it is not used.
The resistivity is blank for 001_Alumina by default.

Enter 1.0 there tentatively. (The value doesn’t affect the simulation)
(This doesn’t affect the simulation) Set the specific heat of 001_Alumina as follows.

Material Name	Specific Heat	Resistivity
001_Alumina	1.0[J/Kg/deg]	1.0[Ωm]

Boundary Conditions

The temperature of the bottom face of the substrate is set to 25[deg] by the boundary condition of T0.
The faces where the strip line ends are set with the “adiabatic” boundary condition, T_Wall.
That keeps the outer boundary condition from being applied on them.
Boundary conditions, V0 and V1, define the voltage at each end of the microstrip line.
The heat transfer to the ambient is defined by the outer boundary condition.
It is not fixed mechanically.

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
T_Wall/Face	Thermal	Adiabatic
T0/Face	Thermal	Temperature	25[deg]
V0/Face	Electric	Electric wall	Waveform: Constant, Voltage: 0.00[V]
V1/Face	Electric	Electric wall	Waveform: Constant, Voltage: 0.01[V]
Outer Boundary Condition *	Thermal	Heat Transfer/Ambient Radiation	Heat transfer coefficient: 10 [W/m2/deg] Ambient temperature: 25[deg]

To set Outer Boundary Condition, go to the [Model] tab

and click [Outer Boundary Condition] .

Results

See Exercise 3 of electric field – thermal coupled analysis for the temperature distribution.

The deformation as a result of Galileo is shown below. The vectors represent the stresses. The unit is [Pa].

The temperature rise at the strip is high and causing the substrate to bend.