On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models
This paper is concerned with the one-dimensional nonlinear theory of elasticity. The authors present a consistent methodology for deriving higher order gradient continuum macroscopic models from the properties of discrete, periodic microstructure. Attention is focused on the model whose energy density involves only the second order gradient of the displacement. The accuracy of the continuum models is evaluated via examples where the boundary value problem of stretching a finite length bar is solved twice, once using the discrete model based on the exact model, and once using the corresponding continuum model based on the approximate one. The force-displacement diagrams and the equilibrium strain profiles for the localized solutions are compared. The stability of the solutions is also investigated.
scientific article; zbMATH DE number 617002
scientific article