Example
This article shows the post-critical analysis. A structural component can be imagined as a flat roof subjected to compression from the outside. When the compression is increased slowly, it is clear that the load is absorbed by the compression stress and transferred to a support.
When a certain compressive load is reached, the structural system becomes unstable and the post-critical failure occurs.
When the load is increased again, it is primarily absorbed by tensile stress in the structural component.
Generally, the second-order analysis cannot detect the post-critical failure due to the linearization of the deformation geometry description.
Further information and examples can be found in [1] and [2].