The purpose of this presentation is to obtain the loading surfaces associated to a TPMS Schwartz Primitive unit 
cell made of NiTi. The unit cell is subjected to cyclic loading. Due to the symmetry conditions, only 
1/16th part of the unit cell is considered. Periodic boundary conditions are applied to simulate a unit cell&nbsp; 
embedded on a full cellular structure, and mixed boudary conditions are applied on the rest of the surface: 
symmetric boundary conditions are applied to the planes of symmetry, an imposed displacement is applied at the bottom surface, and a controlled load is applied at the top surface.&nbsp;Homogenization is&nbsp;performed, so as to obtain volume-averaged values of the stress and strain fields, as well 
as the induced martensite volume fraction. A Python script is used for this matter.&nbsp;These values are representative of the whole unit cell. Based on a criterion to determine the change of phase, the surfaces are obtained on a stress space, establishing the threshold for that phase change.&nbsp;Fitting expressions of the surfaces are obtained. This allows the complex geometry of the unit cell to be substituted by a simpler geometry, and used for large scale simulations.&nbsp;With this in mind, the loading surfaces are expected to change due to the functional fatigue. An initial hypothesis is that the&nbsp; 
surfaces shrink in an axisymmetric way. This is because,&nbsp;as cycles are performed, the martensite volume fraction increases, and that makes the triggering stress for phase transformation&nbsp;diminish. Since it is known that, after a training process, the martensite volume fraction stabilizes, it is expected that the&nbsp;surfaces will reach a minimum and, therefore, stabilized value. These final surfaces would remain for subsequent applied cycles,&nbsp;until structural fatigue would occur. This structural fatigue is not considered in this presentation. The functional fatigue&nbsp;considered for this work is of a low-cycle kind. This is due to the material properties, that make the material complete the training process in a relatively-low number of cycles. For the fatigue loading, a triangular path is input as a controlled loading.&nbsp;An already-established constitutive model is used: the ZM model. This model has the limitation of not considering&nbsp; 
plasticity. Therefore, unusually-high stresses are observed on the simulations. However, it is noted that, in real measurements, these stresses would be alleviated due to the nature of the material itself, which would indeed produce yielding.&nbsp;Another limitation for this case is not considering heat generation, or thermomechanical coupling. Therefore, the frequency with&nbsp;which the load is applied is not a relevant parameter other than for the simulation time. Thus, the heat that would be generated depending on&nbsp;the employed&nbsp;frequency is not taken into account.&nbsp;

Derivation of Loading Surfaces for a Nitinol Triply Periodic Minimal Surface Unit Cell Subjected to Cyclic Loading

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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