###### Abstract
Relevant numerical simulations include the cubic RVE [17], Kelvin model [20; 21; 22; 23], tomography image-based model [24; 25; 26; 27], and 3D random structure model [28; 29; 30; 31]. The Kelvin model, which possesses periodic and symmetric properties, has been widely used for the foam materials with regular geometry in the literature. [PERSON] [20] simulated the yield behaviors of low-density closed-cell polymer foams with an RVE consisting of 1/2 Kelvin cells in height and width and 2 Kelvin cells in depth, which showed that the yield surface of the low-density closed-cell polymer foams was nearly circular on the \(\sigma_{e}-\sigma_{m}\) map. In that paper, the yield point was thought to be reached when a continuous yielded zone in which the equivalent plastic strain of all the elements \(\geq\) 0.01 crossed the foam structure. At this time, change in the stress-strain curve slope would be obvious, or the stress peaked. [PERSON] et al. [22] studied the effect of cell thickness and yield strength of the bulk materials on the failure mechanism of the foam cell, by summing the areas of all the elements that have plasticized to determine the yield point of the foam material. Generally, simulations based on the computed tomography (CT) method could obtain a more realistic performance of foam materials, but it is still difficult to use this method to investigate the effect of the inner structures on the mechanical performance of foam materials. As a compromise, numerical simulations were often carried out for irregular and random foam structures, like the Voronoi structure RVE containing sufficient cells. By applying multiaxial loads on the Voronoi structure of foams, [PERSON] et al. [29] obtained several yield points based on the ratio of plastic dissipation energy to total energy during the loading process. [PERSON] et al. [30] defined the yield points based on the plastic dissipation energy eigenvalue only in their numerical simulation with the Voronoi structure. [PERSON] et al. [31] got the yield points with the same method adopted by [PERSON] and [PERSON] [15], i.e., the yield stress at 0.2% characteristic strain offset. More complicated random structures were also employed to study the mechanical performance of foam materials, e.g., see [PERSON] et al. [32; 33; 34]. The initial yield of foam materials loaded multiaxially is critical to the design of high-performance foam components. For the uniaxial tension and compression of metallic foams, the stress at 0.2% strain offset was usually regarded as a sign of initial yield. However, as mentioned above, there were diverse criteria to determine the initialization of yield for the case of multiaxial loads. Therefore, it is desirable to propose an appropriate method for the yield definition of different types of foam materials subjected to multiaxial loads, to reasonably predict the yield surface. In this work, we aim to explore the yield behavior of closed foams using the Kelvin RVE and random model RVE via the finite element method. To do it, we first determine the yield definition methods under multiaxial load conditions. Several yield definition methods are discussed after the simulations with the two kinds of RVE models. And the simulation results are compared with relevant experimental data to verify the validation of the simulations. Therefore, we can determine the elastic energy criterion at microscopic scales to acceptably identify the yield points of foam materials. And a general yield definition method is presented to determine the yield behavior of the closed-cell foam materials at a macroscopic scale. To verify the applicability of this general yield definition method we, finally, use some random models with different relative densities and inner structures.