三维Cosserat连续体模型与微结构尺寸相关效应的有限元分析

分析了三维Cosserat连续体理论中的应力应变特征,推导了三维Cosserat连续体的有限元方程,基于ABAQUS计算软件提供的用户单元子程序(UEL)接口编写了弹性Cosserat连续体三维20节点有限元程序,并分析了微悬臂梁自由端的挠度问题和微杆扭转问题。通过与基于经典连续体理论的解析解及有限元数值计算结果进行比较,表明所发展的三维Cosserat连续体有限元能有效地模拟微结构尺寸相关效应问题,即随着微结构尺寸与材料内部长度参数的接近,基于Cosserat连续体有限元分析得到的微梁的挠度以及微杆的转角与经典连续体的解析解及有限元解相比越来越小;反之,Cosserat连续体有限元的计算结果与经典连续体的解析解及有限元数值解较为一致。

Three dimensional cosserat continuum model and finite element analysis for the size effect of micro-structure

Micropolar stresses and strains of three-dimensional(3D) Cosserat continuum are analyzed first,then a basic 3D Cosserat continuum theory and 3D 20-node finite element formulations and corresponding user element subroutine based on the subroutine UEL offered by numerical analysis software ABAQUS are developed.The deflection of a micro-cantilever beam and rotational angle of the micro-rod are analyzed by Cosserat continuum FEM and classical continuum FEM and analytical solution respectively.Numerical results demonstrate the effectiveness of 3D Cosserat continuum FEM in modeling size effect of micro-structure:as the size of micro-structure is more closer to the internal length scale,the deflection of a micro-cantilever beam and rotational angle of the micro-rod based on Coseerat continuum FEM are much less than which based on classical continuum theory or FEM; contrarily,the deflection of a micro-cantilever beam and rotational angle of the micro-rod based on Coseerat continuum FEM are much closer to which based on classical continuum theory or FEM.