PSI - Issue 24

Alessandro Pirondi et al. / Procedia Structural Integrity 24 (2019) 455–469 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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difference is contained within 10% and it decreases more sensibly for increasing edge length in comparison to the laminate ply thickness. The incorporation of a SMA ply at the mid-plane in the theoretical model of Betts (2012) that is exact only in the case of pairs of orthogonal plies, is probably at the basis of the difference between FE and MATLAB results. Since the volume fraction of SMA with respect to whole laminate decreases with the square of edge length and linearly with the total thickness, the deviation from the original model due to the presence of SMA ply vanishes for increasing laminate size, that confirms the procedure developed in this work as a fast and reliable tool to estimate the optimal design of SMAC bi-stable laminates subjected to an initial deflection constraint. Table 6. Comparison of obtained from ABAQUS’s model based on the optimal design parameters for the search space given by φ 1 = 75°, φ 2 = 0°. Optimization Set (ABAQUS) (mm) (MATLAB) (mm) Diff. (%) A2-1 20.53 18.5 9.88 B2-1 37.86 35.6 5.79 C2-1 61.58 59.14 3.96 D2-2 62.6 63.5 1.44 E2-2 102.76 101.91 0.827 The stresses in the embedded SMA wires are shown in Fig. 8 with the initial conditions set to the values shown in Table 6. In Fig. 8a, the stress falls back from 884 MPa to 228 MPa, which is however above the stress value required to transform de-twinned into twinned martensite; hence, the initial value of  is preserved for the following actuation step. It can be also deduced that the initial mix of austenite and de-twinned martensite at the beginning of cool-down, transforms into fully detwinned martensite as the final stress level lies above the stress transformation range. The downward peak in Fig. 8a-b, indicates the release of the constraint in out-of-plane direction (demolding).

Fig. 8. (a) Axial stress distribution; (b) Induced strain under thermal load; (c) Evolution of Martensite Volume Fraction in SMA wires; (d) Induced axial Transformation Strain, from Gandhi et al. (2019).

However, still an open issue remains about the fact that the prestraining SMA is imposed as an initial condition into the FE model. In order to account more properly for this point, a prestrain step has to be introduced, that requires a three-dimensional modelling of the wire and of the surrounding composite, thus a full solid or a mixed solid-shell