Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

TL;DR

This paper derives analytical solutions for uniaxial extension in relaxed micromorphic and other generalized continua, aiding in material parameter identification and understanding size-effects.

Contribution

It provides the first full analytical solutions for uniaxial extension in relaxed micromorphic and related continua, including detailed derivations.

Findings

Analytical solutions for uniaxial extension are obtained.

Solutions facilitate identification of material parameters.

Size-effects can be analyzed using these solutions.

Abstract

We derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identification of material parameters of generalized continua which are able to disclose size-effects.