The nonlinear elasticity structural model takes into account geometric nonlinearity in order to simulate  large deformation. In the case of large deformation, the reference configuration is based on initial configuration and all quantities are formulated using total Lagrangian formulation. Consequently, a stiffness matrix becomes a function of displacement. One of the main concepts in such formulation is an introduction of deformation gradient formulation that is the main tool in describing the strains in large displacement formulation.

In summary, the nonlinear elasticity structural model is based on following main concepts:

The relationship between the initial and deformed state is presented as:

Mathematically, the deformation is expressed through the deformation tensor:

(16–22)