Phenomenological dynamic model on two-way shape memory effects of shape memory alloy

A phenomenological dynamic model was constructed for the modeling of two-way shape memory effect in one-dimensional shape memory alloy (SMA) structure. The model was based on the phenomenological theory of thermoelastic phase transformations in SMAs. Hysteresis loops in both mechanical and thermal fields were treated as macroscopic illustrations of martensite transformations and martensite variant re-orientations. A non-convex free energy function was constructed to characterize the phase transformations induced by temperature. Then each of its local equilibriums can be used to represent a phase in the transformations. System states (strain) can be transformed upon external loadings (mechanical or thermal) from one stable equilibrium to another. Then the dynamics of phase transformations can be modeled by simulating the system state transformations. Governing equations for the transformation dynamics were formulated by employing the Lagrange's equation, and were expressed as nonlinear differential equations. One-way shape memory effect was described by a nonlinear ordinary differential equation, and the model for two-way shape memory effect was constructed by taking the weighted combination of different phase transformations. A series of numerical experiments were conducted. Phase transformations induced by both mechanical and thermal loadings were simulated. Hysteresis loops associated with both one-way shape memory effect and two-way shape memory effect under thermal loadings were presented. A single hysteresis loop associatedwith mechanical-induced martensite variant re-orientations and double hysteresis loops associated with the pseudo-elastic effects were presented. The numerical results showed that two-way shape memory effect and pseudo-elastic effect were successfully modeled, which demonstrated the capability of the current model. © 2020, Zhejiang University Press. All right reserved.