周期性蜂窝材料微极等效模型及其微观应力的一种快速算法

将周期性蜂窝材料等效为具有非局部本构的微极连续介质,以解释实验中出现的尺度效应和边界层效应.在评论相关的多种不同方法(能量法、体积平均的均匀化法等)之后,提出了一种基于位移连续和单胞力平衡的推导微极等效本构参数的新方法.以正方形单胞制成的结构为例,在不同的结构与单胞尺寸比下,考虑承受集中点载荷、均布轴力和均布剪力三种载荷工况,比较了离散完全计算、经典连续介质等效和不同微极连续体等效本构的计算结果,建议了较好的微极本构参数值.数值模拟表明,集中点载荷和剪切载荷作用时,在加载点附近和边界部分,微极等效可以显著提高计算精度.最后,给出了一种映射算法,可以根据微极等效连续体分析的结果,快速计算出对应微观单胞构件的应力,以开有圆孔的方板应力集中为例,验证并考察了所提快速算法的有效性和计算精度.

MICROPOLAR CONTINUUM MODELING OF 2-D PERIODIC CELLULAR MARERIALS AND A FAST MAPPING ALGORITHM FOR THE MICRO-STRESS

Micropolar equivalent continuum model is established in this paper to capture the non-local properties of cellular materials and to explain the size effects and boundary layer effects observed experimentally. After comment on a few relative equivalent methods of microplolar continuum for 2-D periodic cellular materials, including energy approaches, homogenization of volume averaging technique and others, we present a united approach to formulate the equivalent micropolar constitutive relation. Taking the square cell structure as an example, the solutions from the standard continuum and three kinds of micropolar continua are compared with the exact discrete simulations of same structures under different ratio of cell length to characteristic length of structures. Three different kinds of loading examples are investigated which are elastic indentation by a point force, distributed pressure and distributed lateral load, respectively. Based on the numerical simulation, micropolar continuum can give much better agreement than those from Cauchy-type continuum under elastic indentation and distributed shear-like load, especially around regions with loading applied and near boundary layer of structures. At last, a fast mapping algorithm for detailed micro-stress distribution in components of cellular materials is developed based on the analysis results with micropolar continuum representation. And the fast algorithm is found to be a reliable method to obtain the detailed local stress information of structures composed of cellular materials by numerical simulation.