The mechanics of phase transformations

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We outline a program to phase transformations by utilizing only the traditional concepts of mechanics together with the new notion of "normal" and "excited" atoms. The meaning of phase transformations is used here in a broad sense to cover phenomena ranging from liquid-vapor transitions and spinodal decomposition to the formation of slip and shear bands, plastic zones and necks, liquid crystal transitions, damage localization, and crack nucleation. In principle, all these phenomena are interpreted within the same theoretical framework by identifying the "excited" atoms and their motion with the predominant microstructure which is responsible for the transformation. For simplicity, we present the basic ideas in one dimension and assess only qualitatively the appropriateness of the model. Roughly speaking, transformations are occurences of a certain instability in the variables defining the body before the transformation. In our approach we retain the same variables but we introduce non-local interactions, usually in the form of gradients, in order to stabilize the behavior and trace the evolution of the system during the transformation. © 1987.

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Mathematical Modelling