## 1 Introduction
The container lifetime (time to failure) in the multi-stacked condition is significantly affected by the level of applied load (stacking load) and by the relative humidity (rh) and moisture content of the container itself (owing to the hygroscopic properties of cellulosic materials). Many researchers [5; 6; 7] have reported that cyclic humidity conditions at the same levels of the applied load lower the container lifetime compared to constant humidity conditions. However, [PERSON] et al. [3] reported that the effects of cyclic and constant humidity conditions differed according to the applied load level. In other words, constant humidity conditions under a high applied load level deteriorated the lifetime more than cyclic humidity conditions, with one reason for this being that the cyclic humidity condi  
Figure 1: Typical creep behavior of a viscoelastic material and Burgers model. tions did not reach the equilibrium moisture condition. However, they stated that testing under cyclic humidity conditions was more appropriate for the packaging industry, as most of the containers were stacked under lower applied load conditions in the supply chain of the container. Many researchers [3; 5; 8] have studied the relationship between the lifetime and secondary creep rate of containers, because the majority of the lifetimes of multi-stacked containers are affected by secondary creep regions. [PERSON] et al. [3] calculated the slope of the linear regression equation for the data corresponding to 10-90% and 20-80% of the period through creep measurement for 21 days; the values obtained were expressed as the secondary creep rates of the failing and non-failing containers within the period, respectively. They reported that the container lifetime was inversely proportional to the secondary creep rate. Long-term stacking tests ranging from several days to several months are required to determine the secondary creep rate of corrugated fiberboard containers. [PERSON] et al. [9] presented a container lifetime estimation method by obtaining the average creep rate through a creep experiment of only 12 h, and correcting it to failure according to the applied load level. The method they proposed starts on the premise that creep failure of a container occurs when the creep strain reaches the quasi-static compression failure strain of the container: \(T=D/R\), where \(T\) = lifetime (time to fail) (min), \(D\) = ASTM D642 failure deformation (mm), \(R\) = average creep rate \([=R_{12}\times P/(100-P)]\) over the entire time up to failure at the applied load level \(P\), \(R_{12}\) = average creep rate in the 12 h test (slope of straight line fitted to creep data), and \(P\) = load expressed as a percentage of the ASTM D642 compression strength (\(CS\)) [10]. As a more recent study, [PERSON] et al. [11] analyzed how creep performance (secondary creep rate) and lifetime of container depend on the container conditions including fill and the area of the container that is exposed for moisture transfer. Regarding the secondary creep rate and lifetime of boxes containing product were significantly smaller than those of other conditions, they said that it was due to the occurrence of out-of-plane displacement due to the internal pressure imparted on the panels by the product. [PERSON] [12] introduced the concept of reliability in predicting the lifetime of the container, and he said that the lifetime is indeed dependent not only on a stacking factor, but also on durability and the variations associated with the material or container. Computer-aided engineering (CAE) prediction technology of compression behavior in multi-stacked home appliance packages equipped with an EPS-based cushioning system is an important technical evaluation tool that can prevent accidents caused by overturning of multi-stacked packages in warehouses. In addition, this tool can help reduce the development period owing to the preliminary review of multi-stacking, improvement of packaging quality, and optimization of packaging materials.