Three-dimensional model of thermomechanical evolution of shape memory materials

We derive a thermodynamically consistent model of the thermomechanical evolution of shape memory materials in three dimensions. The model is based on the linearized strain tensor and the absolute temperature as state variables. It accounts for the viscous and spatially nonlocal effects, and constitutes a generalization of the one-dimensional Falk model. The constitutive equations comply with the entropy inequality. Examples of free energies characteristic for shape memory alloys and noncrystalline materials are given

On diffused-interface models of shape memory alloys

The paper surveys mathematical models of thermo-mechanical evolution of shape memory alloys and related mathematical results. The survey is confined to so-called diffused-interface or phase-field models based on Landau-Ginzburg free energy as a ther-modynamic potential. It includes the well-known models due to Falk, Fremond and Fried-Gurtin. The focus is on a three-dimensional (3-D) generalization of Falk's model based on the linearized strain tensor, absolute temperature and strain tensor gradient. For such model the thermodynamical basis and the recent mathematical results on its well-posedness are presented

Stefan problems in non-cylindrical domains arising in Czochralski process of crystal growth

In this paper we discuss a two-phase Stefan problem with convection in a non-cylindrical (time-dependent) domain. This work is motivated by phase change phenomenon arising in the Czochralski process of crystal growth. The time-dependence of domain is a mathematical description of the situation in which the material domain changes its shape with time by crystal growth. We consider the so-called enthalpy formulation for it and give its solvability, assuming that the time-dependence of the material domain is prescribed and smooth enough in time, and the convective vector is prescribed, too. Our main idea is to apply the theory of quasi-linear equations of parabolic type