Issue 29

M. Marino, Frattura ed Integrità Strutturale, 29 (2014) 96-110; DOI: 10.3221/IGF-ESIS.29.10 109 3 2 2 3 ( ) ( ) = , = in in R D res R D res in in E E E E E E E E                         (28) where = d r         and =| | d r         . C ONCLUSIONS novel constitutive model for the stress-induced martensitic transformations in SMAs has been proposed, accounting for: different behavior for the transformation laws of direct and reverse lattice rearrangement; asymmetric responses in tension and compression (both for transformation and stiffness properties); the possible co-existence of austenite, multi-variant and oriented martensites. Accordingly, the model is suitable for reproducing available experimental data on SMA pseudo-elastic properties. The model is formulated in a generalized energetic framework. By introducing a suitable pseudo-potential of dissipation and by formulating transformation-evolution laws from microscopic equilibrium equations, the fulfillment of the second law of thermodynamics is a-priori satisfied, without the need of implicit algorithms. In order to highlight this feature, the model is developed in detail within a fully explicit framework, easy to be implemented for computational analyses. Obtained results clearly show this feature, highlighting that material parameter identification is straightforward from experimental data, even accounting for a possible non-perfect pseudo-elastic behavior for SMA. The model has been here developed under the assumption of ideal non-hardening behavior. In upcoming works, it will be generalized in order to account for non-linear hardening effects, allowing for an effective comparison with experimental data. Moreover, shape-memory effects as well as non-isothermal response will be accounted for. Accordingly, the effects of non-linear transformation lines in the phase diagram, as well as of temperature-dependent transformation strains, on SMA mechanics will be shown. It is worth pointing out that, within present explicit framework and addressing non- isothermal conditions, the value of / / d r    and / / D R    at the reference temperature T (at = t  ) can be considered in the governing equations at each incremental step. Accordingly, present model does not require to fix a specific form of interpolation functions for transformation lines in phase diagram (assumed piecewise-linear in most modeling approaches), as well as for the temperature-dependence of transformation strains, resulting in a very general and flexible tool for describing very different pseudo-elastic behaviors. A CKNOWLEDGMENTS he author gratefully acknowledges Prof. Franco Maceri, Prof. Giuseppe Vairo and Prof. Michel Frémond for fruitful discussions on this paper. This work was developed within the framework of Lagrange Laboratory, a European French-Italian research group. Present research study was supported by MIUR (PRIN, grant number F11J12000210001). R EFERENCES [1] Shape Memory Alloys. Modeling and Engineering Applications, Lagoudas, D.C. (Ed.), Springer Science+BusinessMedia, LLC, New York, USA, (2008). [2] Songa, G., Ma, N., Li, H.-N., Applications of shape memory alloys in civil structures. Engineering Structures, 28 (2006) 1266-1274. [3] Auricchio, F., Marfia, S., Sacco, E., Modeling of SMA materials: training and two way shape memory effects, Computers and Structures, 81 (2003) 2301-2317. [4] Auricchio, F., Bonetti, E., Scalet, G.,Ubertini, F., Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation. International Journal of Plasticity, 59 (2014) 30-54. [5] Moumni, Z., Zaki, W., Son, N.-Q., Theoretical and numerical modeling of solid-solid phase change: Application to the description of the thermomechanical behavior of shape memory alloys, International Journal of Plasticity, 24 (2008) 614-645. A T