For the Membrane approximation, there is no slit between the two sides of the thin layer. The tangential deformation gradient is computed on the surface as
where ⊗ is the outer product of two vectors,
(N⊗N)ij = NiNj.
Here, λn is the transverse (normal) stretch, and
γ1 and
γ2 are the transverse shears. The vectors
n,
t1, and
t2 are the normal and tangent unit vectors on the deformed surface.
