COMPUTATIONAL HOMOGENIZATION AND MULTISCALE ANALYSIS SHCEME BASED ON CONSISTENT COUPLE STRESS THEORY

Most of the existing computational homogenization methods are based on the classical continuum theory and cannot describe the size effect. To solve this problem, a new computational homogenization method and the corresponding multi-scale analysis scheme are developed based on the consistent couple stress theory to predict the size effects of small-scale composites. Firstly, Hill lemma is extended to the consistent couple stress theory, and two forms of Hill lemma are derived. According to the Hill-Mandel fine micro-macro energy equivalence condition, the average-field theory and the admissibility condition, five different sets of computational homogenization schemes are established respectively based on force-couple boundary condition, force-rotation boundary condition, displacement-couple boundary condition, displacement- rotation boundary condition and periodic boundary condition. On this basis, a finite element simulation is realized via Abaqus/UEL and Abaqus/Python, and the multi-scale analysis scheme for small-scale composites is constructed. The reliability of the scheme is verified through numerical examples. The results show that the multi-scale analysis scheme proposed in this paper has high robustness and can predict the size effect of multi-scale composites effectively.