Density Dependence of the Macroscale Superelastic Behavior of Porous Shape Memory Alloys: A Two-Dimensional Approach

Porous Shape Memory Alloys (SMAs) are of particular interest for many industrial applications, as they combine intrinsic SMA (shape memory effect and superelasticity) and foam characteristics. The computational cost of direct porous material modeling is however extremely high, and so designing porous SMA structure poses a considerable challenge. In this study, an attempt is made to simulate the superelastic behavior of porous materials via the modeling of fully dense structures with material properties modified using a porous/bulk density ratio scaling relation. Using this approach, direct modeling of the porous microstructure is avoided, and only the macroscale response of the model is considered which contributes to a drastic reduction of the computational cost. Foam structures with a gradient of porosity are also studied, and the prediction made using the fully dense material model is shown to be in agreement with the mesoscale porous material model. 1. Introduction Shape Memory Alloys (SMAs) exhibit unusual mechanical properties such as shape memory and superelasticity, which make them very attractive for a wide range of industrial applications, from aerospace to medicine [1, 2]. For more than a decade, not only fully dense but also porous or foamed forms of SMA have been studied because of their additional benefits: low density, high permeability, and energy dissipation properties [3]. The level of foam porosity is selected as a function of the final use of a material while structural applications of porous SMA require low-to-medium porosity foams (pore volume fraction (PVF) ≤ 40%); biomedical applications, such as bone implants [4], need highly porous material with PVF of up to 70%. The properties of porous SMAs are strongly dependent on their porous microstructure, whose length scale is much smaller than that associated with the macroscale response of the whole material. From a numerical point of view, modeling this micro/macro behavior has a tremendous numerical cost. To alleviate the complexity of the micro/macroapproach, that is, the explicit representation of the porous microstructure, researchers have chosen different routes, such as micromechanical averaging techniques [6, 7] or Unit Cell approach [8, 9]. However, those strategies are based on assumptions (low porosity, regular pore distribution, spherically shaped pores, etc.) that are not fully compatible with the biomedical application foams [5] that we are studying in the present paper. To overcome the micro/macro numerical cost while reconciling the needs of biomedical foams, we have