Nonlinear Static Stress studies build upon the foundations of Static Stress studies. The basis for the theoretical background is outlined in the Static stress theoretical background section. Where Nonlinear Static Stress studies are differentiated is in their handling of material and geometric nonlinearities.
One key assumption held by Hooke's Law (F=kx), is that the material stiffness, k, is held constant throughout the analysis. Depending on the material in question and the degree to which the material is stressed, this can be an inaccurate assumption. In Nonlinear Static Stress studies, the stiffness is updated at every equilibrium iteration. Therefore, determining the global response of the structure becomes an iterative process, requiring the incrementation of applied loads and boundary conditions.
Hooke's Law also assumes a linear (small displacement) response of the structure to the applied loads. Once again, depending on the material in question and the degree to which the material is strained, this can be an inaccurate assumption. In large geometric deformations, strains become a nonlinear function of the displacement gradients. Any load increment must be solved for the deformed structure, not the original structure.