基于三维模型的蜂窝材料有效弹性性能研究  

Investigation on Effective Elastic Properties of Honeycomb Materials Using Three-dimensional Model

作　　者：徐耀玲[1] 龙晓彭 Yaoling Xu;Xiaopeng Long(Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures of Hebei Province,Yanshan University,Qinhuangda,066044)

机构地区：[1]燕山大学河北省重型装备与大型结构力学可靠性重点实验室,秦皇岛066004

出　　处：《固体力学学报》2022年第1期40-49,共10页Chinese Journal of Solid Mechanics

摘　　要：采用三维模型预测了传统六角形蜂窝材料和带圆环结点六角形蜂窝材料的有效弹性性能.利用有限元法并结合周期边界条件计算了材料代表性体积单元的平均应力,进而由平均场理论获得了两种蜂窝材料全部的有效弹性常数.将传统蜂窝材料的计算结果与已有梁模型的计算结果和试验数据进行了对比,结果表明三维模型比梁模型具有更高的精度,分析了梁模型误差产生的原因.带圆环结点蜂窝材料的计算结果表明,在保持材料相对密度不变的前提下,通过调整结点圆环壁厚和蜂窝壁厚的比值可显著提高蜂窝材料的面内刚度.Due to some excellent mechanical properties such as lightweight, high specific strength, high specific stiffness, etc., honeycomb materials have been widely used in many lightweight constructions. The effective elastic constants of honeycomb materials are necessary mechanical parameters in designing such lightweight constructions;hence, an accurate estimate of the effective elastic constants of honeycomb materials has great practical application value. For simplicity, beam models are usually adopted in existing studies. The existing results show that the in-plane effective elastic moduli and Poisson’s ratios predicted by beam models have large deviations from the experimental data, which implies the unreliability of the results derived from beam models in some cases. In this paper, the effective elastic properties of conventional hexagonal honeycomb materials and the hexagonal honeycomb materials with circular joints are investigated using the three-dimensional model. By employing the three-dimensional finite element analysis combined with periodical boundary conditions, average stresses in the representative volume elements of the two honeycomb materials are obtained, and then all the effective elastic constants, i.e., all elastic moduli and Poisson’s ratios, of the two honeycomb materials are derived using the mean-field theory. The numerical examples reveal transversely isotropic characteristics of these two honeycomb materials. Comparisons of the present results of conventional hexagonal honeycomb with the existing results derived from beam models and test data show that the three-dimensional model has higher accuracy compared with beam models. The causes of errors of beam models are discussed. The in-plane stiffness of the hexagonal honeycomb with circular joints can be improved dramatically by adjusting the ratio of the wall thickness of the circular joint to the honeycomb wall thickness under fixed relative density. The present results and comparisons show the necessity of three-dimensional model in pr

关 键 词：蜂窝材料 圆环结点 有效弹性性能 周期边界条件 有限单元法 

分 类 号：TB383.4[一般工业技术—材料科学与工程]