PSI - Issue 47

582 Stefano Rodinò et al. / Procedia Structural Integrity 47 (2023) 579–588 Carmine Maletta / Structural Integrity Procedia 00 (2018) 000–000 Where � and � are the moments of inertia of the SMA and matrix layers, � and � are the Young’s moduli, is the curvature radius of the composite beam. Substituting eqs. () - () into eq. Errore. L'origine riferimento non è stata trovata. ) and considering eq. (5) give: � �ℎ � �ℎ � � 2 � � � � � � � � (9) The curvature 1  can be directedly obtained from eq. (9): 1 � � �ℎ � �ℎ � � 2 � � � � � � � � � (10) With the assumption of perfect bonding at the SMA-matrix interface, the strain compatibility condition at the interface can be written as: �� � �� (11) Where �� and �� are the deformations at the SMA-matrix interface that can be obtained from axial and bending components: �� �� � � � � ℎ � 2 (12) �� � � � � � � � ℎ � 2 � � �ε � (13) Where � is the initial pre-strain of the SMA wires and � is the transformation strain. Substituting eqs. (12) and (13) into eq. (11) and considering eq. (5) gives: � � � ℎ � ℎ � � � 1 � � � �� 2 1 �ℎ � �ℎ � �� � �ε � � 0 (14) Substituting eq. (9) into eq. (14) gives: � � � ℎ � ℎ � � � 1 � � �� � � �ℎ � �ℎ � � � 4 � � � � � � � � � � � �ε � � 0 (15) The average stress in the SMA layer � � � � �  ) of the composite beam as obtained from thermal activation can be directly obtained from the following equation: � ��ε � � � �� ℎ � ℎ � � � 1 � � � � � �ℎ � �ℎ � � � 4 � � � � � � � � � � �� (16) The beam curvature can be computed from eq. (9) by the stress obtained from eq. (15): 1 � � �ℎ � �ℎ � � 2 � � � � � � � � � (17) Equation (17) can be rewritten as a function of the average stress � as follows: 4