### The Influence of Microstructure and Specimen Size Ratio on the Elastic Modulus of a Bar Element

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#### Abstract

By introducing higher order strain gradient terms and an internal length parameter (the gradient elastic coefficient) into the constitutive stress-strain relation for the analysis of a bar, a corresponding elastic modulus is herein derived, which includes the classical and gradient elastic terms. With this, the micro-scale influence of the material is readily captured and the Elastic modulus is shown to depend on changes in the ratio between the dimension of the microstructure and the bar element specimen the so called size effect. A numerical study is presented as illustration. *Copyright © 2014 Praise Worthy Prize - All rights reserved.*

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