Modeling of Shape Memory Alloy Wire Meshes Using Effective Lamina Properties for Improved Analysis Efficiency

Shape memory alloy (SMA) wire meshes are being investigated for their potential effectiveness as active layers in self-folding origami laminates. The currently studied meshes consist of two orthogonal sets of equally spaced parallel SMA wires. The modeling of self-folding laminates with SMA wire meshes becomes computationally demanding at full scale due to the expenses of accurately representing the bending segments of the SMA meshes. Modeling the wires as beam, shell, or three-dimensional entities can be used for such purposes; however, those options become difficult to implement due to the small dimensions of the mesh compared to the full scale self-folding system and the algorithmic complexity of considering the application of heating power to discrete wire regions. A solution to this problem is to model the SMA meshes using an equivalent lamina representation. In this work, an effective lamina model for the representation of the SMA wire meshes that accounts for thermoelastic and inelastic phase transformation behavior is developed. A reduced order version of the effective lamina model is implemented and validated against finite element simulations of an SMA wire mesh considering the same underlying 3D constitutive model. The results show that the effective lamina model accurately predicts the behavior of the fully modeled SMA wire mesh. Future work includes the calibration of the full version of the model and its implementation in a finite element framework.