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The Cauchy and Born hypotheses for crystals. (English) Zbl 0567.73112
Phase transformations and material instabilities in solids, Proc. Conf., Madison/Wis. 1983, Publ. Math. Res. Cent. Univ. Wis. Madison 52, 61-77 (1984).
[For the entire collection see Zbl 0557.00011.]
This paper is concerned with the study of the deformations involved in phase transformations in solids. To relate changes in atomic positions to macroscopic deformation, the molecular theories of elasticity of crystals use the hypotheses introduced by Cauchy or Born. In Cauchy’s hypothesis the atomic motion and the gross motion are the same. Born assumed that the lattice vectors deform as would material line elements, subject to the macroscopic deformation. In the present paper the author studies the applicability of these hypotheses to describe deformations encountered in phase transformations.
Reviewer: D.Ieşan

MSC:
74A60 Micromechanical theories
74M25 Micromechanics of solids
82D25 Statistical mechanical studies of crystals
82B26 Phase transitions (general) in equilibrium statistical mechanics
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids