Modeling of Shape Memory Alloys and Application to Porous Materials

In the last two decades the number of innovative applications for advanced materials has been rapidly increasing. Shape memory alloys (SMAs) are an exciting class of these materials which exhibit large reversible stresses and strains due to a thermoelastic phase transformation. SMAs have been employed in the biomedical field for producing cardiovascular stents, shape memory foams have been successfully tested as bone implant material, and SMAs are being used as deployable switches in aerospace applications. The behavior of shape memory alloys is intrinsically complex due to the coupling of phase transformation with thermomechanical loading, so it is critical for constitutive models to correctly simulate their response over a wide range of stress and temperature. In the first part of this dissertation, we propose a macroscopic phenomenological model for SMAs that is based on the classical framework of thermodynamics of irreversible processes and accounts for the effect of multiaxial stress states and non-proportional loading histories. The model is able to account for the evolution of both self-accommodated and oriented martensite. Moreover, reorientation of the product phase according to loading direction is specifically accounted for. Computational tests demonstrate the ability of the model to simulate the main aspects of the shape memory response in a one-dimensional setting and some of the features that have been experimentally found in the case of multi-axial non-proportional loading histories. In the second part of this dissertation, this constitutive model has been used to study the mesoscopic behavior of porous shape memory alloys with particular attention to the mechanical response under cyclic loading conditions. In order to perform numerical simulations, the model was implemented into the commercial finite element code ABAQUS. Due to stress concentrations in a porous microstructure, the constitutive law was enhanced to account for the development of permanent inelasticity in the shape memory matrix. First, an idealized model of porous material has been used and samples with different material porosities have been constructed. With this simulation method, the complex interaction between porosity, local phase transformation and macroscale response has been evaluated. Then, a real experimental microstructure has been used to build a three-dimensional model of the porous SMA. The impact of microstructural characteristics on the average macroscopic response has been investigated. The results have significant implications for use of porous SMAs in biomedical and structural applications.