PSI - Issue 47

Stefano Rodinò et al. / Procedia Structural Integrity 47 (2023) 579–588 Carmine Maletta / Structural Integrity Procedia 00 (2018) 000–000

581

3

2.2. SMA-composite bending model The active composite material with embedded SMA wire is modelled as an equivalent bimaterial plate (see Fig. 1), according to Choi et al. [37], having the same volume fraction of SMA elements. More specifically, for a plate with length (L) and width (b), the active SMA layer thickness (h a ) as follows: ℎ � �� π � 4 (4) here d is the SMA wire diameter and n is the total number of embedded wires.

Fig. 1. Bimaterial plate equivalence.

The internal reactions acting on the matrix cross section can be represented as a force F m and a bending moment M m [38]. Similarly, F a and M a represent the force and bending moment acting on the active SMA layer (see Fig. 2). If no external forces are applied the internal reactions are generated only by thermally-induced shape recovery of the SMA layer. The force and moment equilibrium conditions can be written as follows: � � � (5) � ℎ � 2 � � ℎ � 2 � � � � (6)

Fig. 2. Schematic depiction of the internal force distribution on the matrix/SMA bi-material plate

If no plastic deformations occur, the internal moments M a and M m can be obtained as follows: � � � �

(7)

� � � � � �

(8)