Issue 29

V. Sepe et alii, Frattura ed Integrità Strutturale, 29 (2014) 85-95; DOI: 10.3221/IGF-ESIS.29.09 86 the possibility of undergoing greater overall strains as well as higher specific energy absorption under dynamic loading conditions due to the possibility of wave scattering. In the biomedical field, thanks to their high biocompatibility [4] and their capacity to exhibit high strength, NiTi foams have been tested as bone implant materials [5], effectively exhibiting a considerable amount of bone ingrowth. In particular, these materials display unique characteristics such as: relatively low stiffness, useful to minimize stress shielding phenomenon, shape recovery effect, that facilitates implant insertion and ensures good mechanical stability within the host tissue, elevated osteoconductivity and better osseointegration and osteoconductivity than bulk NiTi alloys. In the last years, applications of porous SMA in the field of Civil and Mechanical Engineering have also been considered. The potential applications of porous SMA exploit their ability to carry significant loads and their high energy absorption capability. In fact, the porous SMA shows a higher specific damping capacity under dynamic loading conditions with respect to the dense SMA, because the pores facilitate an additional absorption of the impact energy. In order to correctly reproduce the behavior of the porous SMA, the development of accurate models describing their properties is needed. Several papers have been published concerning the modeling of porous SMA (e.g. [6-8]). The porous SMA material can be treated as a composite with SMA as the matrix and pores as the inclusions. In order to derive the mechanical response of porous SMA, micromechanical averaging techniques have been developed in the available literature, as for instance [9, 10]. Indeed, different micromechanical and homogenization techniques, usually applied to study composites can be used to model porous SMA, such as the Eshelby dilute inclusion technique or the Mori-Tanaka scheme [11, 12] or the self- consistent method. An interesting approach that has been adopted to study the behavior of porous materials is based on the assumption of having a periodic distribution of pores. In this case, the problem can be solved by using a computational homogenization technique based, for instance, on nonlinear finite element analyses of a single unit cell with suitable boundary conditions. The behavior of porous SMA under cyclic loading conditions has been studied in [13], where the constitutive law has been enhanced to account for the development of permanent inelastic strains due to stress concentrations in the porous microstructure. Aim of the present contribution is to propose a micromechanical study of porous SMA. In particular, the response of porous SMA is derived by performing the nonlinear finite element micromechanical analysis for the typical repetitive unit cell, considering periodicity conditions. The constitutive model, proposed in [15] and [16] and able to reproduce the main properties of dense shape memory alloys response, is adopted in order to simulate the behavior of the porous SMA. The constitutive response and the dissipation energy capability of the porous Nitinol are investigated for several values of porosity. Numerical applications are developed in order to assess the ability of the presented procedure to well capture the overall behavior of the special heterogeneous material, correctly reproducing the pseudoelastic effect., a key feature of the shape memory alloys. P OROUS SMA MODELING he porous SMA is a composite material in which voids can be considered as inclusion in a dense SMA matrix. The study of the mechanical response of porous SMA can be conducted performing micromechanical analyses which accounts for the presence of a random distribution of voids characterized by different shape and dimensions. In this study, developed in the framework of small strains, the simplifying hypothesis of regular, i.e. periodic, distribution of voids is introduced: in other words, it is assumed that all the voids have the same dimension and shape. In such a way, the study can be limited to the analysis of a unit cell (UC) which is representative of the heterogeneous material and that completely accounts for the geometry and material properties of the constituents of the composite. Such a simplified approach allows to derive the influence of the void volume fraction on the mechanical response. SMA constitutive model Concerning the modeling of dense SMA material, the model initially proposed by Souza et al. [14] and modified first by Auricchio and Petrini [15] and, then, by Evangelista et al. [16] is adopted to reproduce the shape memory alloys behavior. In the following discussion, the Voigt notation is adopted, so that second order tensors are represented as vectors and fourth order tensors as matrices. In particular, the strains and the stresses are reported as vectors with 6 components, while symmetric 6×6 matrix defines the elastic constitutive matrix. The use of this notation is preferred as it enables a straightforward implementation in a numerical code. T