A New Micromechanical Approach of Micropolar Continuum Modeling for 2-D Periodic Cellular Solids Considering Displacement Compatibility and Equilibrium of Force

• 1、Department of Engineering Mechanics, Dalian University of Technology

Abstract：Micropolar equivalent continuum model has been proposed in literatures to capture the non-local properties of cellular materials and to explain the size related effects. However, different effective micropolar constants are observed in different papers for the same microstructure. Obviously, they give different results of equivalent analysis for the same cellular solid, some of which have great errors compared with the discrete analysis for the same cellular solid. In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of 2-D periodic cellular materials. The new united approach takes both displacement compatibility and equilibrium of force and moment into consideration via the adoption of Taylor series expansion of the displacement and rotation fields and the extended averaging procedure with explicit enforcement of equilibrium in micromechanical analysis of the cell structure in the cellular materials. The micro-polar constitutive parameters are deduced with the new approach. The structure made of 2-D cellular solids with Hexagonal cells with shear traction on top surface is analysized numerically. The solutions from three kinds of micropolar continuum modeling with different effective micropolar constants by different authors are compared with the exact discrete simulations of the same structures. It is found that the micropolar constants developed in this paper give the most satisfying results of the equivalent analysis for hexagonal cells.

Keywords： Cellular Material Micropolar continuum Size effect Equivalent properties