The Electric Currents in Shells Interface
The Electric Currents in Shells (ecis) interface (), found under the AC/DC>Electric Fields and Currents branch when adding a physics interface, is used to compute electric fields, currents, and potential distributions in thin conducting layered shells under conditions where inductive effects are negligible; that is, when the skin depth is much larger than the studied device. It supports stationary, time-dependent and frequency domain modeling on faces in 3D.
The electric potential can be located either on the selected surface or in a product space spanned by the surface and the physical thickness of the shell (using an extra dimension). For conductive shells, the physics interface solves a current conservation equation based on Ohm’s law using the scalar electric potential as the dependent variable. For dielectric layers the interface solves Gauss’ law (it effectively turns into a local Electrostatics interface).
The Electric Currents in Shells interface is very similar to The Electric Currents in Layered Shells Interface. The main difference is the default mode. The Electric Currents in Layered Shells Interface is set to be layered by default, while the Electric Currents in Shells interface is set to be nonlayered by default.
This interface supports layered shell features, which means each boundary in the 3D geometry may represent a number of thin layers with different electrical properties. Potential variations in the normal direction (in between and inside layers) are supported. For a general description of layer and interface selections, see Layer and Interface Selection Tools. For more information, see the section on how to set up a Layered Material node in the COMSOL Multiphysics Reference Manual.
For a more extensive introduction to the physics and equations implemented by this physics interface, see The Electric Currents Interface, and the Theory for the Electric Currents Interface. Additional information is available in Theory for the Electrostatics Interface chapter and The Electric Currents, Single Layer Shell Interface chapter.
Settings
The Label is the default physics interface name.
The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is ecis.
Boundary Selection
By default, all boundaries are available for the application of The Electric Currents in Shells Interface. Select the Restrict to layered boundaries check box to make the interface applicable only if a layered material is defined on the boundary. If a layered material (Material with Layer thickness specified, Single Layer Material, Layered Material Link, or Layered Material Stack) is available, its name is then displayed beside the boundary index (for example, slmat1), otherwise the boundary is marked as not applicable.
Shell Properties
The default setting of the combo box Shell type is the main difference between The Electric Currents in Shells Interface and The Electric Currents in Layered Shells Interface, where the former is set to be Nonlayered shell by default and the later is set to be Layered shell by default.
When the Nonlayered shell option is selected, the interface treats the thickness as a multiplicative factor which enters the conservation of surface currents.
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If the Restrict to layered boundaries check box is not selected in the Boundary Selection section, a nonlayered material may be defined on the selected boundaries, and the Thickness Lth can be set as a user defined value or expression. This value overrides the values set in the material nodes.
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You can visualize the selected layered materials and layers in each layered material by clicking the Layer cross section preview and Layer 3D preview buttons.
When the Layered shell option is selected, the Extra Dimension tool is used to solve the equations through the thickness of a layered material. Depending on other settings, it can describe the physics of objects where electric potential vary both tangentially and perpendicularly (through the thickness).
The thickness of the layered material should be set as follows, depending on the type of material:
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In a Material node, the Layer thickness can be in the table found under the Material Contents section of the material Settings window. This automatically adds a Shell subnode under the Material node, transforming it as a layered material.
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When the layered material is a Single Layer Material, the Thickness is set in the Layer Definition section of the Shell Property Group window.
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For a general Layered Material, added through a Layered Material Link or a Layered Material Stack, the Thickness is set in the Layer Definition section of the Settings window. Several layers may be defined in the table, and the Thickness should be defined for each of them. The total thickness of the layered material is the sum of all the layers thicknesses.
Note that the Layered shell option should be used whenever a layered material is applied on the boundaries, because the thickness is part of the material settings.
Clear the Use all layers check box to apply The Electric Currents in Shells Interface on some layers only. Select a Layered material from the list (the interface is then applicable only on the boundaries where this latter material is defined), and clear the check boxes corresponding to layers where the interface should not be applied in the Selection table.
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The layer thickness variable, ecis.ds, used in the weak equations, is the product of the thickness set in the Shell Properties section, ecis.lth, and the scale factor ecis.lsc, which is equal to 1 by default, and can be overridden by a user defined value in a single layer material.
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The layer thickness variable, ecis.ds, is defined in all dimensions, and is unrelated to the Out-of-plane thickness of the layered material, htlsh.d, which is only available in 2D.
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See Layer and Interface Selection Tools.
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You can provide material parameters with a through-thickness variation by explicitly or implicitly using expressions containing the extra dimension coordinate as described in Using the Extra Dimension Coordinates.
The desired selection for the physics interface may correspond to boundaries with different layered materials. This means that a single physics interface can accommodate several different stacking sequences.
See Layered Material, Layered Material Link, Layered Material Stack, Layered Material Link (Subnode), and Single-Layer Materials in the COMSOL Multiphysics Reference Manual for details on the definition of layered materials.
Discretization
Select the shape order for the Electric potential dependent variable — Linear, Quadratic (the default), Cubic, Quartic, or Quintic. For more information about the Discretization section, see Settings for the Discretization Sections in the COMSOL Multiphysics Reference Manual.
Dependent Variables
The dependent variable is for the Electric potential V. The name can be changed but the names of fields and dependent variables must be unique within a model.