Structures can behave linear or nonlinear. A Structural linear response shows a linear relationship between stress and strain, while a structural nonlinear response shows a nonlinear relationship between stress and strain.
In the case of elastic-plastic material behavior, the material behaves first elastic and then plastic. Both elasticity and plasticity can be associated to a linear or nonlinear material response.
The elasticity is a reversible material behavior that can be linear or nonlinear, during which the considered structure return to his original shape when the applied stress is released. The plasticity is in opposition an irreversible material behavior.
For linear material behavior a linear analysis could be directly applied.
Considering a elastic-plastic material behavior where plasticity happens after the yield point, a nonlinear analysis should be applied.
When simulating a elastic-plastic material behavior, a linear analysis is valuable before the yield point if the elastic response part is linear; otherwise a nonlinear analysis is valuable to describe more precisely the nonlinear elastic part of material behavior.
After the yield point a nonlinear analysis should be used to describe the plastic material response.
For hyper-elastic materials a nonlinear analysis is also valuable.
