Global solution to the full one-dimensional Frémond model for shape memory alloys

✍ Scribed by Pierluigi Colli; Jürgen Sprekels

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 759 KB
• Volume: 18
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670180504

✦ Synopsis

In this paper, we prove the existence and uniqueness of the solution to the one-dimensional initialboundary value problem resulting from the Fr6mond thermomechanical model of structural phase transitions in shape memory materials. In this model, the free energy is assumed to depend on temperature, macroscopic deformation and phase fractions. The resulting equilibrium equations are the balance laws of (linear) momentum and energy, coupled with an evolution variational inequality for the phase fractions. Fourth-order regularizing terms in the quasi-stationary momentum balance equation are not necessary, and, as far as we know for the first time, all the non-linear terms of the energy balance equation are taken into account.