we all know the linear hookes law as f=kx where f is the force applied on a spring and x is the displacement and k is the spring stiffness. All springs need not behave linearly. suppose a spring behaves non linearly What is the theory that calculates the deflection for a non linear spring when a force f is applied. Basically i believe non linear finite element analysis is based on this non linear spring theory. in a non linear spring f will not be proportional to x but may be proportional to square of x or cube of x or some power of x.