A study on the two second-order strain gradient theories

There are various strain gradient theories derived fromphenomenal theory and nonlocal continuum mechanics. Meanwhile, there are twopopular second-order strain gradient theories in which strain gradient termwas introduced into the constitutive law with positive and negative signsrespectively. In this paper, these two theories are discussed in the aspectof formula derivation, energy expression, and application fields. By usingthe 18-DOF triangle strain gradient plan element (RCT9+RT9) and axisymmetricelement (BCIZ+ART9) which can pass C^0\hbox-1 patch test, the elasticpull-out processes of the reinforced concrete bond specimen and thedeformation of a cantilever beam are simulated to compare the limitation ofthe two theories in the analysis of microstructures.