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arXiv · 1901.02813

Exact and numerical solutions to a Mindlin microcontinuum model

Armando Majorana·Rita Tracinà
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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.

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Armando Majorana, Rita Tracinà. 2019-01-09. Exact and numerical solutions to a Mindlin microcontinuum model. https://arxiv.org/abs/1901.02813

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