Shape Memory Alloy Engineering

6.3. Three-dimensional Phenomenological Constitutive Model for SMA

6.3.1. Finite Strain Constitutive Model

In this section, the phenomenological thermomechanical finite strain SMA constitutive model proposed by Evangelista et al.⁵² is presented. The model is deduced introducing a free energy function depending on internal variables able to describe the state of the phase transformation and to represent the history dependence of SMA behavior.

The model is based on the assumption of the local multiplicative split of the deformation gradient into an elastic part and a phase transformation part, denoted as F_e and F_t, respectively.^93,94 Accordingly:

F(X,t)=Fe(X,t)Ft(X,t)

(6.1)

at a typical material point position X∈Ω.

In particular, the proposed model assumes ...