Physical and Mathematical Representations of Couple Stress Effects on Micro/Nanosolids

In the present paper, for linear elastic materials, effects of couple stresses on micro/nanosolids are physically discussed and mathematically represented in the context of the classical, the modified and the consistent couple–stress theories. Then, an evaluation is provided showing the validity and the limit of applicability of each one of these theories. At first, the possible couple stress effects on mechanics of particles and on continuum mechanics are represented. Then, a reasoning comparison with examples is performed to discuss and evaluate the way that each one of these theories represents the couple stress effects. In the context of the classical couple–stress theory, two higher-order material constants are introduced in addition to the conventional ones to capture the microstructure rigid rotation effects. Recently, two alternative theories, the modified couple–stress and the consistent couple–stress theories, with only one additional material constant are introduced with contradictory points of view. Authors of these two alternative theories gave apparently strong motivations for their opposed points of view. Therefore, through the present paper, it will be convenient to analyze the essential points of view based on which these alternative theories are proposed since they lead to exactly opposed conclusions. Thus their essential points of view are discussed and evaluated showing their consistency with the fundamental concepts of the couple stress effects. It has been shown that the scientific bases of these two alternative theories are not consistent with the representation of the couple–stress effects on micro/nanocontinua. Based on discussions and results through the paper, both the modified theory and the consistent theory represent, only, simplifications for the classical couple–stress theory but they did not able to well represent the possible effects of couple stresses and they are limited for only two categories of linear elastic materials problems. This demolishes the scientific points of view based on which the two theories are proposed.