For the Solid approximation on interior thin layers, the displacements between the two sides of the boundary are decoupled. The two boundaries are then connected by elastic and viscous forces proportional to the relative displacements and the corresponding material model.
By using the notation u1 = down(
u) and
u2 = up(
u), so
u1 represents the displacement of the downside (bottom), and
u2 is the displacement of the upside (top) of the thin layer, the average displacement of the midsurface reads
With this notation, the normal vector N points from the downside (bottom) toward the upside (top).
where d is the thickness of the thin layer, and the quantity
ue/d represents its strain.
When Layered is selected in the
Thin layer type list, the gradient through the normal direction is approximated as
where z is the extra dimension coordinate, that varies between
0 and the layer thickness
d.