Deformation recovery effects derived from finite J₂ flow models

Abstract

In an explicit sense of thermodynamical consistency, we propose a non‐linear combined hardening elastoplastic J₂ flow model to display deformation recovery effects. With this model, we show that any axial strain of a uniaxially bar loaded well beyond initial yielding is recoverable upon removal of the applied load. As such, each process of application/removal of the axial load results in a deformation recovery loop. In a broad sense, we demonstrate that loops of any given shape may be generated by specifying suitable hardening functions. It follows that deformation recovery effects with various shapes of recovery loops may be derived from non‐linear combined hardening elastoplastic J₂ flow models. In particular, we show that there exist hardening functions generating flag‐like recovery loops. The latter are associated with the remarkable deformation recovery effects of shape memory alloys. This suggests that the finite recoverable deformation behaviour (superelasticity or pseudoelasticity) of shape memory alloys may be characterised straightforwardly by classical elastoplasticity models from a direct phenomenological standpoint.

Keywords:

• Shape memory material
• Finite deformation
• Elastoplasticity