Open AccessThe tightness of the teeth, considered as a problem concerning the equilibrium of a thin incompressible elastic membrane
Author(s) -
J. L. Synge
Publication year - 1933
Publication title -
philosophical transactions of the royal society of london. series a, containing papers of a mathematical or physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9258
pISSN - 0264-3952
DOI - 10.1098/rsta.1933.0012
Subject(s) - elasticity (physics) , membrane , displacement (psychology) , compressibility , mechanics , mathematics , materials science , physics , chemistry , composite material , psychology , biochemistry , psychotherapist
A tooth may be regarded as a rigid body, held in a rigid socket by a thin membrane— theperiodontal membrane orpericementum —which fills the space between the tooth and the bone, and is attached to each. This membrane, whose average thickness is only 0.23 to 0.25 mm. (0.0091 to 0.0099 in.), is called upon to supply the tractions necessary to resist the forces applied in biting or chewing. An interesting problem in the theory of elasticity is thus suggested, namely, the determination of the displacement of the tooth and the strain and stress in the membrane, corresponding to the application of assigned forces to the crown of the tooth. We are obviously entitled to treat the problem mathematically as that of an infinitely thin membrane, but we shall have to make other simplifications in order to reduce the problem to a manageable form.