Homogenized Shell
The Homogenized Shell feature takes the material properties from one or more selected layers, and determines their effective material properties. It integrates the conductivity in the direction normal to the shell (in the direction of the extra dimension), taking the local layer thickness into account:
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where d refers to the total thickness of all layers involved. For a discrete set of layers having their own uniform material properties, this integral effectively translates to a sum of conductivities, multiplied by their corresponding local layer thickness:
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This represents a parallel connection of resistors. The Varying Thickness subfeature can be used to locally affect the degree to which a particular layer contributes to the sum.
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If composite, layered materials and general anisotropy are not of interest to you and you want to solve an in-shell current conservation problem (as with The Electric Currents, Single Layer Shell Interface), use a Homogenized Shell feature with a Single Layer Material.
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The Varying Thickness subfeature will allow you to set a spatially or temporally varying thickness (to model material deposition and such).
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The electric potential is automatically continuous among adjacent Homogenized Shells. More information about continuity in Electric Currents, Layered Shell interface can be found in the chapter Electrical Continuity in the Electric Currents, Layered Shell Interface.
The resulting material properties are then used in a current conservation problem, that only considers the potential gradients tangential to the shell (in-plane conservation law):
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where the product dσeffET is effectively the surface current density Js in A/m. ET is the tangential electric field, and Qs represents a volumetric source of current. Without sources, the right-hand side becomes zero, and in-plane current should be conserved.
When applied to a single layer, the Homogenized Shell is virtually identical to the traditional, nonlayered Current Conservation feature in the Electric Currents, Single Layer Shell Interface.
Layer Selection
Select the layers to be included in the integral for the effective material properties.
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For a general description of layer and interface selections, see The Layer Selection Section.
Conduction Current
By default, the Electrical conductivity σ (SI unit: S/m) of the layers is defined as From material. If you select User defined, the same user defined value will be applied to all selected layers.