The Experimental Evidence for Higher Gradient Theories

Abstract

In this document, it will be attempted to summarize the currently available experimental evidence for the need of higher gradient continuum theories. They allow to capture size effects, e.g., within the elastic behavior of materials with an internal substructure, which gives rise to additional length scale parameters. These are not available in elastic theories of the Cauchy–Boltzmann type. First, some theoretical background information regarding the additional parameters on higher gradient continuum theories will be given. Then the pertinent constitutive equations of second gradient materials for both solids and fluids will be presented, such that they agree with nomenclature used in the experiments. Finally, experimental data showing the size effects for various materials are compiled stemming from different sources. Some own results are also included, and the literature is extensively reviewed.