A simple nonlinear model to simulate the localized necking and neck propagation

• A model simulating necking and neck propagation is proposed.
• Two-phase model under uniaxial loading is developed.
• A damage function depending on the stored energy function is assumed.
• A constitutive law for damaged polymeric materials is formulated.
• Neck propagation is modeled through a purely energetic criterion.

This paper deals with the equilibrium problem in nonlinear dissipative inelasticity of damaged bodies subject to uniaxial loading and its main purpose is to show the interesting potentialities offered by the damage theory in modeling the necking and neck propagation phenomena in polymeric materials. In detail, the proposed mechanical model is a two-phase system, with the same constitutive law but with different levels of damage for each phase. Despite its simplicity, it is shown that the model can straightforwardly reproduce the overall load–elongation curve provided by experimental tensile tests by involving only five parameters of clear physical meaning.