## 1 Introduction  
Consumer-packaged goods are handled and transported predominantly in unit load form, commonly using wooden pallets and corrugated fiberboard boxes [1, 2]. Pallets are key throughout most supply chains, from agricultural operations to retailers [3]. The design of pallets for material handling has evolved from a trial-and-error method to the development of advanced modeling systems [4, 5, 6, 7, 8]. The need for better models is supported by the material consumption present in pallet manufacturing and by the overall resources utilized in transportation operations [9, 10]. Estimates place the number of pallets in circulation at over 2 billion units in the United States and 6.8 billion units globally [3, 11]. In 2016 in the United States, more than 500 million new pallets were manufactured, and 341 million were repaired for continued use. The volume of wood consumed for pallet manufacturing represented 21.8% of the total lumber production in the United States. Pallets for material handling represent one of the largest segments in consumption of sawn hardwoods in the United States, with 45% of the total production being dedicated to them [12]. A critical need exists for efficient use of the natural resources consumed to support supply chains. Proper design of each component in the system is required. The load carrying capacity of most pallets is determined using a uniformly distributed load for each support condition of use, such as warehouse racking or floor stacking [13, 14]. Research conducted as early as 1982 shows that when pallets are loaded with specific payloads, instead of uniform loads, pallet bending is reduced due to the redistribution of the stresses on the pallet towards the supports [4; 15]. Further exploration of this redistribution of stress across the pallet's top deck, known as the load bridging effect, has been conducted mostly through physical tests measuring the change in pallet deflection. The international standard, ISO 8611-Part 3 [16], recognizes the effect of load bridging by allowing for the determination of a maximum working load of a pallet for a specific payload. Research efforts have been made to further understand which aspects of the pallet, or the payload, significantly influence load bridging for specific payload configurations. One of the first comprehensive studies was conducted in 1997. They first determined five differing levels of rigidity for a payload and then measured how much the deflection changed under each level [17]. Although a clear effect in the results was observed (deflection decreased in direct relation to the payload rigidity), the results can only be considered preliminary since the effect of individual factors were not isolated from each other. The isolated effect of multiple palletizing characteristics such as containment force [18], box size [19; 20; 21], flute size [19], box contents [22], and interlock stacking [23] were previously investigated. All of these studies used physical testing which involved the construction of unit loads or segments of unit loads and subsequent laboratory measurements. Physical testing of unit loads can provide valuable information but has drawbacks. Physical testing is a time-intensive endeavor, interactions between variables are hard to investigate, and the control of experimental variables is not a simple task. Simulations using the finite element method have been used extensively in the mechanical engineering field and recently have been widely adopted in the packaging field. Research includes finite element analysis (FEA) of different packaging materials, such as wood [24], corrugated board [25; 26; 27; 28], paperboard [29; 30] and multiple others [31], including the extensive use of finite element models in the development of food packaging [32; 33; 34; 35]. The use of finite element analysis has also become commonplace when designing pallets for material handling systems. Wooden pallets can be designed using commercial software that are already available; most of which are based on finite element models [36].