This thesis is devoted to the study of a thermomechanical model describing the macroscopic behavior of shape memory alloys. The analyzed model takes into account the non-isothermal character of the phase transition, as well as the existence of the intrinsic dissipation. The first law of thermodynamics, the balance of momentum in its quasi-static form, the evolution equation for the internal variables (the volume fraction of martensite), together with the second principle of thermodynamics (the entropy inequality), lead to a partial differential equations system. In the circular cylindrical case the problem reduces to the following ordinary differential system: The unknown data are: the temperature θ at the surface of the body, the total fraction β of the martensite in the body, and the axial elongation ε of the sample in the Ox3 direction. The stress σ is supposed to be given. These all are real functions depending only on the time variable t > 0. The constants τ, Γ, L, C, E, g, p, q, T0, Ta, ΔT are all positive, T0 > Ta, Γ < L/C, and σ± := p(T0 - Ta + θ + βΔT) ± q. We prove uniqueness of solutions in a large class of functions spaces (abstract derivation structures), as well as existence and regularity in several such spaces.
Daniel Kressner, Christoph Max Strössner
Michaël Unser, Sebastian Jonas Neumayer, Pol del Aguila Pla
Bernard Kapidani, Rafael Vazquez Hernandez