###### Abstract  
In this paper, the yield behavior of closed-cell foams under multiaxial load conditions is investigated via finite element analysis on the representative volume element (RVE) scale by using the regular Kelvin of RVE and random models of RVE, respectively. Several different definitions of yield are considered in the study. By benchmarking the simulations with the experimental data in the literature, it is shown that the elastic energy criterion is shown to be suitable for the definition of the yield point of closed-cell foams under different stress states. Based on the micro-scale elastic energy, which can be readily obtained by numerical simulation, a general yield definition is proposed to determine the yield behavior of the closed-cell foam materials at macroscopic scales. To test the adaptability of this general yield definition, we analyze multiple random models with different relative densities and inner structures. The results indicate that this general yield definition method can be used for different models, even applied to continuum materials. yield behavior; yield surface; foam material; multiaxial loads; yield  
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experiment. Only the yield points near the \(\sigma_{e}\) axis could be obtained on the \(\sigma_{e}-\sigma_{m}\) map in the experiments with butterfly specimens, where \(\sigma_{e}\) is the Mises stress and \(\sigma_{m}\) represents the mean stress. To obtain more yield points, more experiments with cylindrical specimens subjected to different types of load were performed such as uniaxial tension and compression, shear, combined hydro-compression, and hydrostatic tests [6; 7; 8; 9; 10; 11; 12]. [PERSON] and [PERSON] [6] performed a range of axisymmetric compressive experiments for cylindrical aluminum alloy foam specimens, in which the yield point was defined as a 0.3% offset axial strain of the specimens according to the experimental results, and the yield surfaces of the foam material were presented in the stress space of \(\sigma_{e}-\sigma_{m}\). [PERSON] et al. [8] measured the failure of open- and closed-cell aluminum foams under axisymmetric compression and hydrostatic compression using cylindrical specimens, where the failure point was identified as the peak load in the axial direction if existed, or as the stress at the intersection of the slopes of the linear elastic and plateau region. The yield surfaces in the tests could be described by two phenomenological surfaces models: the Druker-Prager criterion and self-similar model in [6]. [PERSON] et al. [7] studied the yield behavior of PVC foam under proportional axisymmetric compressive loading with various axial-to-radial stress ratios. They obtained the yield points as the intersection of the extrapolations of the linear elastic and stress plateau lines. In the study presented by [9], uniaxial compressive, hydrostatic compressive, and proportional axisymmetric compressive yield behaviors of the aluminum alloy foam were measured and the yield point was considered as the stress at a 0.04% offset plastic strain. Some researchers performed their experiments with cubic specimens [6; 7; 13; 14; 15; 16]. [PERSON] et al. [13; 14] conducted uniaxial, biaxial, and axisymmetric tests for polyurethane and aluminium replicated foams, of which the yield point corresponded to 0.2% strain offset in the plot of the Mises stress \(\sigma_{e}\) versus the Mises strain \(\epsilon_{e}\), and the yield surface depended on all three invariants of the stress tensor. [PERSON] and [PERSON] [15] put forward a characteristic stress-strain definition to deal with their experiment results. Both [PERSON] et al. [16] and [PERSON] et al. [19] used 0.2% strain offset on the characteristic stress-strain curve as the yield point. Because of the limitations of the experiment, numerical simulation was necessary for the study of foam materials yield performance.