The Thermoelasticity Interface
The Thermoelasticity multiphysics interface () can be found under the Structural Mechanics branch () when adding a physics interface using the Model Wizard or the Add Physics window. The thermoelastic effect results in local cooling of material under tension and heating of material that is compressed. Irreversible heat transfer occurs between the warm and cool regions of the solid, producing mechanical losses, which can be important, particularly for small structures.
When this multiphysics interface is added, the Model Builder tree structure is populated with two physics interfaces (Solid Mechanics and Heat Transfer in Solids), and two Multiphysics couplings (Thermal Expansion and Temperature Coupling).
In the Settings window for the Solid Mechanics interface, the Structural Transient Behavior is set to Include inertial terms by default. In the Settings window for Thermal Expansion, under the section Heat Sources, the check box for Thermoelastic damping is enabled by default.
On the Study Types for Thermoelasticity
Since this multiphysics interface is aimed at computing the thermoelastic damping of MEMS structures under vibration, it only makes sense to analyze the model in the time or frequency domain. Furthermore, for the frequency-domain study types, it is necessary to first include a stationary study step in order to establish the baseline temperature (the linearization point for the temperature field). Therefore, only the following three study types are recommended for the Thermoelasticity multiphysics interface: Time Dependent; Thermal Perturbation, Eigenfrequency; and Thermal Perturbation, Frequency Domain.
On the Temperature Variable for Thermoelasticity
As mentioned above, for the frequency domain study types, there are two components of the temperature variable: the baseline temperature and the harmonic temperature (which varies around the baseline). To specify the baseline temperature at a boundary, use the Temperature boundary condition. To specify the harmonic temperature at the boundary, right-click the Temperature node and select the Harmonic Perturbation subnode.
Thermoelastic Damping in a MEMS Resonator: Application Library path MEMS_Module/Actuators/thermoelastic_damping_3d
On the Constituent Physics Interfaces
The Solid Mechanics interface is intended for general structural analysis of 3D, 2D, or axisymmetric bodies. In 2D, plane stress or plane strain assumptions can be used. The Solid Mechanics interface is based on solving Navier’s equations, and results such as displacements, stresses, and strains are computed.
The Heat Transfer in Solids interface provides features for modeling heat transfer by conduction, convection, and radiation. A Solid model is active by default on all domains. All functionality for including other domain types, such as a fluid domain, is also available. The temperature equation defined in solid domains corresponds to the differential form of the Fourier's law that may contain additional contributions like heat sources.
On the Couplings
The coupling occurs on the domain level, where two physical effects occur:
•
The temperature from the Heat Transfer interface acts as a thermal load for the Solid Mechanics interface, causing thermal expansion.
•
The tension and compression from the Solid Mechanics interface acts as a heat source for the Heat Transfer interface, causing local cooling and heating.
These effects are implemented by the combination of the two multiphysics couplings mentioned above.
Coupling Features
When physics interfaces are added from the Model Wizard or using the Add Physics window then the appropriate coupling feature is automatically added to the physics interface. However, the physics interfaces can be added one at a time, followed by the coupling features.
For example, if single Solid Mechanics and Heat Transfer in Solids interfaces are added, then COMSOL Multiphysics adds an empty Multiphysics node. You can then choose the coupling features: Thermal Expansion and Temperature Coupling.
Coupling features are available from the context menu (right-click the Multiphysics node) or from the Physics toolbar, Multiphysics Couplings menu.
Physics Interfaces and Coupling Features
Use the online help in COMSOL Multiphysics to locate and search all the documentation. All these links also work directly in COMSOL Multiphysics when using the Help system.
Coupling Features
The The Fluid-Solid Interaction Interface node is described in the section The Thermal Stress Interface in the Structural Mechanics User’s Guide.
The Temperature Coupling node is described in the section The Joule Heating Interface in the COMSOL Multiphysics Reference Manual.
Thermoelastic Damping in a MEMS Resonator: Application Library path MEMS_Module/Actuators/thermoelastic_damping_3d