In the present study, considering the random distribution of carbon nanotubes in polymethylmethacrylate (PMMA) polymer, a multi-scale finite element method has been developed to investigate the mechanical behavior of these materials. In order to make realistic assumptions, the interface zone between the nanotubes and the matrix is simulated using the interfacial zone model (IZM), with its parameters obtained by calibrating the finite element model results with the results of experimental tests. Tensile tests and scanning electron microscopy (SEM) were used to study the mechanical properties and morphology of the PMMA foam samples reinforced with 0 wt%, 1 wt% and 2 wt% carbon nanotubes. Experimental results show that by adding 1 wt% and 2 wt% carbon nanotubes to PMMA foam, the tensile strength of the foam increases by 8% and 22%, respectively, compared to pure foam. Based on the results of the finite element models, the optimum percentage of the carbon nanotubes is 3.3 wt%, which gives the optimum modulus and tensile strength of 87 MPa and 4.02 GPa, respectively. The finite element model developed in the present study shows good agreement with the experimental results. Therefore, the impact of effective parameters on the mechanical properties of the foam can be easily studied based on the finite element method (FEM) results.

在本研究中，考虑到聚甲基丙烯酸甲酯（PMMA）聚合物中碳纳米管的无规分布，已经开发了一种多尺度有限元方法来研究这些材料的机械性能。为了做出现实的假设，使用界面区域模型（IZM）模拟了纳米管与基质之间的界面区域，并通过校准有限元模型结果和实验测试的结果来获得其参数。拉伸测试和扫描电子显微镜（SEM）用于研究用0 wt％，1 wt％和2 wt％碳纳米管增强的PMMA泡沫样品的力学性能和形态。实验结果表明，通过向PMMA泡沫中添加1 wt％和2 wt％的碳纳米管，泡沫的拉伸强度分别提高了8％和22％，相比纯泡沫。根据有限元模型的结果，碳纳米管的最佳百分含量为3.3 wt％，其最佳模量和拉伸强度分别为87 MPa和4.02 GPa。本研究开发的有限元模型与实验结果吻合良好。因此，可以基于有限元方法（FEM）的结果轻松研究有效参数对泡沫力学性能的影响。