
Accession Number : AD0661201
Title : THEORIES OF ELASTIC CONTINUA AND CRYSTAL LATTICE THEORIES.
Descriptive Note : Technical rept.,
Corporate Author : COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
Personal Author(s) : Mindlin,R. D.
Report Date : AUG 1967
Pagination or Media Count : 16
Abstract : This paper is concerned with the relations between lattice and continuum theories of the elastic behavior of perfect crystals. In the case of a simple Bravais lattice, it is shown in what way the differential equations of motion of successively higher order 'strain gradient' theories of elasticity correspond to successively shorterwave approximations to the difference equations of motion of the lattice and how the additional material constants, which appear in the gradient theories, are related to the force constants of the lattice. In the case of a lattice with a basis, a new theory of elasticity is given for the long wave approximation, as distinguished from the long wave, low frequency approximation. It is also shown how to obtain shorterwave continuum approximations to the equations of motion of a lattice with a basis. Finally, for both types of lattice, it is shown how the difference equations of motion may be converted to differential equations which yield the same dispersion relations, as do the difference equations, for all wave lengths. (Author)
Descriptors : (*CRYSTAL LATTICES, *ELASTIC PROPERTIES), STRAIN(MECHANICS), CONTINUUM MECHANICS, DIFFERENCE EQUATIONS, EQUATIONS OF MOTION
Subject Categories : Crystallography
Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE