Plasticity Model for Superelastic Materials

The plasticity model for superelastic materials is based on the uniaxial stress-strain response, as shown in Figure 1. Such materials (e.g., Nitinol) are in the austenite phase under no loading conditions. Austenite is assumed to follow isotropic linear elasticity. On loading the material, the austenite phase starts transforming into martensite beyond a certain stress. Martensite is assumed to follow an elastoplastic response, with elasticity characterized by the linear elastic model and the plastic behavior represented by the Drucker-Prager model. Martensite exhibits plastic behavior after full transformation.

Uniaxial superelastic-plastic response of Nitinol type materials.

In this model the total strain increment, $\mathrm{\Delta }\epsilon ,$ is assumed to be the sum of the elastic strain increment, $\mathrm{\Delta }{\epsilon }^{el}$, the increment in transformation strain, $\mathrm{\Delta }{\epsilon }^{tr}$, and the increment in plastic strain, $\mathrm{\Delta }{\epsilon }^{pl}$:

The increment in plastic strain is calculated using a nonassociated flow rule:

where $G^{pl}$ is the plastic flow potential, $G^{pl}$ is equal to the Mises equivalent stress, $q,$

The yield surface, $F^{pl}$, is assumed to follow the Drucker-Prager formulation with hardening driven by the equivalent plastic strain, ${\overline{\epsilon }}^{pl}$:

where $p$ is the pressure and $\beta$ is the friction angle. The initial yield stress is the stress at which the transformation of austenite into martensite ends, ${\sigma }_{tL}^E\mathrm{.}$