DERIVATION OF LOADING SURFACES FOR A NITINOL TRIPLY PERIODIC MINIMAL SURFACE UNIT CELL SUBJECTED TO CYCLIC LOADING

This paper intends to describe the process of derivation of loading surfaces with respect to phase transformation, when a structure is subjected to cyclic loading. This structure is realized as a Schwarz Primitive unit cell, for which only 1/16^th part is considered, due to the symmetry conditions. Displacement boundary conditions are applied to realize the periodicity of the unit cell, thus simulating the presence of adjacent unit cells. A homogenization of the stress fields is done, so as to obtain volume-averaged values that represent the whole domain. One limitation of the employed constitutive model is not considering plasticity. The large stresses observed in the results would be alleviate in a real application by plastic deformation. Another limitation of the model is not considering a thermomechanical coupling. Therefore, the heat that would be generated depending on the frequency employed is not taken into account. Thus, the frequency of the applied displacements only plays a role in the simulation time. One hypothesis is that the curves in a stress space will shrink as more cycles are performed, due to a higher martensite volume fraction. This is a consequence of functional fatigue. The curves are indeed observed to shrink in an axisymmetric way, due to the lack of phenomena to shift the curves along any of the axis.