In damage modeling, a concept of effective stress (σ, *) is defined as σ, * = (1-D) σ,, where D is defined as a scalar damage variable.
Further, there are many ways in which the damage formulations are derived like Strain equivalence, Stress equivalence, Energy equivalence. The strain equivalence formulations reduce the material stiffness (E) by a factor of (1-D) to apply the damaging effect. The resulting equation for the stress is σ, = (1-D)E x ɛ,. On the other hand, the energy equivalence, which is considered as a more generalized approach gives, σ, = ((1-D)^2)E x ɛ,.
It is obvious from the equations that both approaches give different results for stresses.
My question is, which of these approaches are correct?. And what really confuses me is that the energy equivalence method, which is known to be the more generalized approach, doesnt result in the same stress values as the strain equivalence method. I have to choose one of these damage formulations, for my task. I am confused which one to choose.