A 3D mesoscopic model for the closed-cell metallic foams subjected to static and dynamic loadings Qin Fang * , Jinhua Zhang, Yadong Zhang, Hao Wu, Ziming Gong PLA University of Science and Technology, Nanjing, Jiangsu 210007, China article info Article history: Available online 4 November 2014 Keywords: Metallic foam Closed-cell Mesoscopic model The entrapped air Numerical simulation abstract This paper presents a three-dimensional (3D) mesoscopic model to investigate the responses of closed- cell metallic foams subjected to static and dynamic loadings, especially focusing on the 3D mesoscopic model and the mechanical response. In the first part of this paper, we propose the algorithms to generate the 3D convex polyhedrons modeling the pores with random shapes in closed-cell metallic foams. The 3D mesoscopic model of the foams and the finite element grid are proposed using the ‘take & place’ algorithm and the mapping algorithm. In the second part of this paper, the finite element grid is coupled into the commercial hydrocode LS-DYNA and the ALE analysis approach considering the fluid (the entrapped air) and the structure (the cell-walls) interaction is used. The plastic kinematic model and the linear polynomial equation of state are employed to simulate the cell-walls and the entrapped air, respectively. The responses of closed-cell aluminum foams subjected to static and dynamic compression at high strain rates are simulated by the proposed model and analysis approach. It is demonstrated that the simulated results agree well with test data and the entrapped air plays an important role in the responses when the foams undergo large deformation. Finally, numerical simulations are conducted using the validated approaches, focusing on the effects of mesoscopic configurations (such as the pore size, average density and cell wall strength) on the dynamic responses and the mesoscopic failure patterns. The results show that the collapse and the fracture of the cell walls behave differently under static and high strain rate loadings. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction Metallic foam is a lightweight cellular material and has been used extensively in engineering [1,2,4]. It has been revealed that metallic foam is a kind of heterogenous materials and dependent on the rate of loading [5]. In the past decades, the increasing in- terest was focused on the characteristics of static and dynamic properties [6e8]. Lots of studies, such as the experimental re- searches [9e11] and the numerical simulations [12e14], have been conducted to reveal the capability under impact and blast loadings. It has been improved significantly for the mechanical studies of the metallic foam. For the closed-cell metallic foam, it is composed of air entrapped in the matrix in manufacture. It behaves multiscale characteristics inherently and heterogeneity, which originates from the randomly distributed cell [15]. Attention to new methods is extremely important for predicting the mesoscopic performance. Santosa et al. [16] developed a new model and Li et al. [17] utilized the Voronoi tessellation technique to study the crushing behavior of the cell walls. Zheng et al. [14] and Zhang et al. [18] chosen the three dimensional Voronoi structures to model the inner geometric structure of closed-cell metallic foams and found that there is an important correlation between the pore irregularity variation and the plastic response variation. These studies give significant improvement to the researches of the static and dynamic proper- ties of metallic foams. It also reveals that the development of the model that can consider the microstructure of cellular materials is critical for the further investigations. As is known to all, the aluminum foam is a highly complex porous material. It contains a very high percentage of air entrapped within the matrix. The mechanical performance is modified greatly for the presence of the air. As pointed by Ma [3,19] and Srivastava [20], the air entrapped in the closed-cells has an influence on the deformation of the cell wall. The deformation and collapse of cell- wall compresses the inside air, resulting in air pushing the cell walls. The air flow is found to be essentially affected by * Corresponding author. Tel./fax: þ86 25 84871530. E-mail address: fangqinjs@139.com (Q. Fang). Contents lists available at ScienceDirect International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng http://dx.doi.org/10.1016/j.ijimpeng.2014.10.009 0734-743X/© 2014 Elsevier Ltd. All rights reserved. International Journal of Impact Engineering 82 (2015) 103e112