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:
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:
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.
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.
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.