The concept of material forces in phase transition problems within the level-set framework |
| |
Authors: | Antonios I Arvanitakis Vassilios K Kalpakides |
| |
Institution: | 1.Department of Materials Science and Engineering, Laboratory of Mathematical Modeling and Scientific Computing,University of Ioannina,Ioannina,Greece |
| |
Abstract: | The dynamics of a phase transition front in solids using the level set method is examined in this paper. Introducing an implicit
representation of singular surfaces, a regularized version of the sharp interface model arises. The interface transforms into
a thin transition layer of nonzero thickness where all quantities take inhomogeneous expressions within the body. It is proved
that the existence of an inhomogeneous energy of the material predicts inhomogeneity forces that drive the singularity. The
driving force is a material force entering the canonical momentum equation (pseudo-momentum) in a natural way. The evolution
problem requires a kinetic relation that determines the velocity of the phase transition as a function of the driving force.
Here, the kinetic relation is produced by invoking relations that can be considered as the regularized versions of the Rankine–Hugoniot
jump conditions. The effectiveness of the method is illustrated in a shape memory alloy bar. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |