多层次等效的Mori-Tanaka法预测含空腔点阵增强芯层的等效弹性模量

提出了兼具力学和声学性能的夹层吸声复合材料-含空腔点阵增强夹芯结构；为了预测含空腔点阵增强结构芯层的等效弹性模量，建立了包含空腔、点阵增强柱和泡沫基体的三相复合材料的细观力学多层次等效数理模型，结合点阵增强柱和空腔周期性分布的特点建立代表性体积单元，利用Mori-Tanaka方法进行两次单相夹杂等效处理，获取了含空腔点阵增强芯层等效弹性模量的解析解，与试验数据和细观力学有限元法结果对比均吻合较好。采用有限元软件ANSYS建立了含空腔点阵增强夹芯结构的实际模型和等效模型，并将芯层等效模量解析结果作为等效模型芯层的材料参数，计算弯曲变形和固有频率并进行对比分析，弯曲变形位移和中低频固有频率的相对误差不超过2%，满足工程精度要求。进一步利用该等效方法，分别探讨了点阵增强柱和空腔体积比对芯层等效弹性模量的影响规律。结果表明，上述方法能较准确地预测含空腔点阵增强结构芯层的等效弹性模量，且数理模型清晰，公式简单，计算快速。

Prediction of equivalent modulus of lattice-reinforced core materials with cavities using the multi-level equivalent Mori-Tanaka method

A lattice-reinforced sandwich structure with cavities was presented, which had prospects of the integration of both mechanical and acoustic properties. In order to predict the equivalent modulus of lattice-reinforced core materials with cavities, a multi-level equivalent micromechanical mathematical model was built, which was made up of cavities, lattice reinforcements and foam matrices. With the reinforcements and cavities distributing periodically in the core, the representative unit of the equivalent model was established. Based on the Mori-Tanaka method, the single-phase inclusion equivalent was performed twice and the equivalent modulus of lattice-reinforced core materials with cavities were obtained which agree well with the experimental results and those determined using the FEM method. The numerical simulation was then conducted via the ANSYS code package to obtain the bending deformations and the natural frequencies of both the actual model and the equivalent mode, and the equivalent modulus of the core was used as the material parameter of the core of the equivalent model. The simulation results conform highly with each other and the relative errors of both the bending deformation displacements and the natural frequencies at low frequency are less than 2%, which satisfy the precision requirement in engineering.On this premise, further research was conducted to investigate the effects of reinforcements and cavities volume ratio on the equivalent modulus of the core. The results indicate that the above method can predict equivalent modulus of lattice-reinforced core materials with cavities accurately and quickly with a clear mathematical mode and simple formulas.