The Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects

TL;DR

This paper extends the Armstrong-Frederick cyclic hardening plasticity model by incorporating Cosserat micropolar effects, establishing coercivity, and proving the existence of solutions with improved regularity.

Contribution

It introduces a micropolar extension of the Armstrong-Frederick model that ensures coercivity and develops a new solution concept for non-monotone, non-associated rate-independent plasticity models.

Findings

Established coercivity of the extended model

Proved existence of solutions with better regularity

Developed a weak energy-type inequality for the flow rule

Abstract

We propose an extension of the cyclic hardening plasticity model formulated by Armstrong and Frederick which includes micropolar effects. Our micropolar extension establishes coercivity of the model which is otherwise not present. We study then existence of solutions to the quasistatic, rate-independent Armstrong-Frederick model with Cosserat effects which is, however, still of non-monotone, non-associated type. In order to do this, we need to relax the pointwise definition of the flow rule into a suitable weak energy-type inequality. It is shown that the limit in the Yosida approximation process satisfies this new solution concept. The limit functions have a better regularity than previously known in the literature, where the original Armstrong-Frederick model has been studied.