A Phenomenological One-Dimensional Model Describing Stress-Induced Solid Phase Transformation with Permanent Inelasticity

The use of shape memory alloys for a large number of applications in many fields of engineering has given rise to a great interest of researchers on an exhaustive modeling of their macroscopic behaviour.

Most of the models proposed in the literature, however, consider a perfect pseudo-elastic behaviour (i.e. no residual strains), which is experimentally proved to be only an approximation. This paper addresses a new one-dimensional model able to include also permanent inelasticity effects, whose main features are shown by many numerical tests.

ACKNOWLEDGEMENTS

The authors would like to thank Doctor Ulisse Stefanelli (Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, Pavia) for the fruitful discussions on the mathematical framework of the model. This work has been partially developed within the joint French-Italian “Lagrange laboratory” project and has been partially supported by the Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR) through the research program “Shape-memory alloys: constitutive modeling, structural analysis and design for innovative biomedical applications,” as well as by the European Project HPRN-CT-2002-00284 “New Materials, Adaptive Systems and their Nonlinearities. Modelling, Control and Numerical Simulation.”