Modeling Thermal Stresses
Some MEMS devices are fabricated by sequential depositions of thin or thick films. This process introduces thermal residual stresses in the structures due to the mismatched thermal expansivity of the deposited layers and the substrate as well as the difference between the deposition and operating temperatures.
Thermal stresses in a single added layer can be modeled in multiphysics interfaces using a coupled multiphysics interface that include the Solid Mechanics interface by adding a The Fluid-Solid Interaction Interface subnode under the Multiphysics node (in the Solid Mechanics interface you can also add it as subnode to the material model). A reference temperature, Tref, for zero thermal strain must be specified, and the operating temperature, T, is set by selecting a heat transfer interface in a multiphysics model, which sets up this temperature coupling automatically, or by selecting a temperature as a model input (that is, temperatures generated by other physics interfaces can be selected or a user-defined value or expression for the temperature can be supplied), if the thermal expansion is defied in the Solid Mechanics interface. If the device is operated at a constant temperature, then The Solid Mechanics Interface should be used with T specified as a user-defined constant value in the model input. If temperature gradients resulting from external heat sources are present in the structure then The Thermal Stress, Solid Interface is the natural choice because this physics interface couples heat transfer with the Solid Mechanics interface (in this case you only need to specify the strain reference temperature Tref in the Thermal Expansion subnode; the temperature coupling to the heat transfer interface is set up by the Thermal Stress multiphysics interface). Finally for Joule-heated structures, The Joule Heating and Thermal Expansion Interface make it possible to use arbitrary zero strain reference temperatures, which enables the inclusion of thermal stress in addition to the Joule heating effects. For this physics interface you only need to specify the strain reference temperature Tref in the Thermal Expansion subnode as in the Thermal Stress interface.
Thermal stresses in multilayered structures can also be modeled. As an example, consider a trilayer structure (a substrate plus two deposited layers), modeled using the Solid Mechanics interface with a Thermal Expansion subnode. For the first added layer, the zero strain temperature should be set to the deposition temperature of this layer, but the solution temperature (set through the model input), should be set to the deposition temperature of the second layer. A second study step should then be added with the output of the first study step supplied as an initial stress (this requires two Solid Mechanics interfaces to be added to the model, and some adjustment of the solver settings). For the second study step the zero strain reference temperature is chosen as the deposition temperature of the second added layer and the solution (model input) temperature should be set to the operating temperature. This process can naturally be extended to any number of deposited layers.
Thermal Stresses in a Layered Plate: Application Library path MEMS_Module/Actuators/layered_plate