The deformation gradient F is defined as the gradient of the current coordinates with respect to the original coordinates:

See the Lagrangian Formulation section for details.

Here, ∇tu is the displacement gradient computed using the tangential gradient on the reference surface, N is the normal vector to the undeformed surface, and ⊗ is the outer product of two vectors, (a⊗b)ij = aibj. The term is the so-called normal gradient, that can be approximated by different approaches.