Abstract
This paper is concerned with the relations between discrete and continuum theories of the elastic behavior of perfect crystals. The point of view adopted is that the validity of any extension of the classical theory of elasticity, intended to accommodate effects of the atomic structure of crystalline solids, can be tested by comparison with an appropriate lattice theory. The particular test to be applied is how well and to how short wave lengths the dispersion relation for plane waves, deduced from the continuum theory, reproduces that for the lattice.
Paper prepared for IUTAM “Symposium on the Generalized Cosserat Continuum ...”, August, 1967.
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© 1968 Springer-Verlag Berlin Heidelberg
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Mindlin, R.D. (1968). Theories of Elastic Continua and Crystal Lattice Theories. In: Kröner, E. (eds) Mechanics of Generalized Continua. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-30257-6_38
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DOI: https://doi.org/10.1007/978-3-662-30257-6_38
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