Exact and numerical solutions to a Mindlin microcontinuum model
Abstract
In this paper we consider a one-dimensional Mindlin model describing linear elastic behaviour of isotropic materials with micro-structural effects. After introducing the kinetic and the potential energy, we derive a system of equations of motion by means of the Euler-Lagrange equations. A class of exact solutions is obtained. They have a wave behaviour due to a good property of the potential energy. Numerical solutions are obtained by using a weighted essentially non-oscillatory finite difference scheme coupled by a total variation diminishing Runge-Kutta method. A comparison between exact and numerical solutions shows the robustness and the accuracy of the numerical scheme. A numerical example of solutions for an inhomogeneous material is also shown.
Cite
@article{arxiv.1901.02813,
title = {Exact and numerical solutions to a Mindlin microcontinuum model},
author = {Armando Majorana and Rita Tracinà},
journal= {arXiv preprint arXiv:1901.02813},
year = {2019}
}