The tightness of the teeth, considered as a problem concerning the equilibrium of a thin incompressible elastic membrane

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Abstract
A tooth may be regarded as a rigid body, held in a rigid socket by a thin membrane— the periodontal membrane or pericementum —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.

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