Todhunter, I. (1886) A History of the Theory of Elasticity and of the Strength of Materials from Galileo to the Present Time. Vol. 1, Cambridge University Press, New York.

has been cited by the following article:

• TITLE: Euler-Lagrange Elasticity with Dynamics

  AUTHORS: H. H. Hardy

  KEYWORDS: Elasticity, Stress, Strain, Infinitesimal Deformations, Finite Deformations, Discrete Region Model

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.13, December 23, 2014

  ABSTRACT: The equations of Euler-Lagrange elasticity describe elastic deformations without reference to stress or strain. These equations as previously published are applicable only to quasi-static deformations. This paper extends these equations to include time dependent deformations. To accomplish this, an appropriate Lagrangian is defined and an extrema of the integral of this Lagrangian over the original material volume and time is found. The result is a set of Euler equations for the dynamics of elastic materials without stress or strain, which are appropriate for both finite and infinitesimal deformations of both isotropic and anisotropic materials. Finally, the resulting equations are shown to be no more than Newton's Laws applied to each infinitesimal volume of the material.