Stability of crystalline solids—I Continuum and atomic-lattice considerations
by
Ryan S. Elliott, Nicolas Triantafyllidis, John A. Shaw.
in
Journal of the Mechanics and Physics of Solids, 54(1):193–232, 2006.
Category: Journal Article
Keywords: Phase transformation; Vibrations; Finite strain; Stability and bifurcation; Asymptotic analysis
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Abstract:
Many crystalline materials exhibit solid-to-solid martensitic phase transformations in response to certain changes in temperature or applied load. These martensitic transformations result from a change in the stability of the material’s crystal structure. It is, therefore, desirable to have a detailed understanding of the possible modes through which a crystal structure may become unstable. The current work establishes the connections between three crystalline stability criteria: phonon-stability, homogenized-continuum-stability, and the presently introduced Cauchy-Born-stability criterion. Stability with respect to phonon perturbations, which probe all bounded perturbations of a uniformly deformed specimen under ‘‘hard-device’’ loading (i.e., all around displacement type boundary conditions) is hereby called ‘‘constrained material stability’’. A more general ‘‘material stability’’ criterion, motivated by considering ‘‘soft’’ loading devices, is also introduced. This criterion considers, in addition to all bounded perturbations, all ‘‘quasi-uniform’’ perturbations (i.e., uniform deformations and internal atomic shifts) of a uniformly deformed specimen, and it is recommend as the relevant crystal stability criterion.
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