A review of some plasticity and viscoplasticity constitutive theories

The purpose of the present review article is twofold:•recall elementary notions as well as the main ingredients and assumptions of developing macroscopic inelastic constitutive equations, mainly for metals and low strain cyclic conditions. The explicit models considered have been essentially developed by the author and co-workers, along the past 30 years;•summarize and discuss a certain number of alternative theoretical frameworks, with some comparisons made with the previous ones, including more recent developments that offer potential new capabilities.