computationally intensive method (Hutton, 2004). When FEA was in its early years, mainframe computers, which were considered a powerful tool for engineering design and analysis, were used (Hutton, 2004). The first finite element software code that was developed during the 1960’s was NASTRAN, which was capable of handling thousands of nodal field variable computations (Hutton, 2004). However,
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in the last two decades there has been a progressive growth in the development of commercial finite element codes. This has enhanced their use in modelling complex phenomena, which consequently makes them attractive and increases their versatility for engineering design. According to Robertson (2012), the advent of finite element analysis has made the task of designing and manufacturing in food packaging easier and rapid. This has also resulted in enormous flexibilities and efficiencies through a more thorough design analysis of variables such as stresses and the mechanical performance as a whole. In today’s computational environment, most of these FEA codes can be implemented on desktop computers and engineering workstations to obtain solutions to large problems in static and dynamic structural analysis, heat transfer, fluid flow and electromagnetics. Five of the commercial FEA codes that are more commonly used, particularly in food packaging are discussed below and examples of research using the software given. Although the FEA software packages highlighted have proved very useful in packaging research, we do not necessarily provide endorsement for these FEA software packages.
3.4.1 ANSYS
The flexibility and robust design analysis of ANSYS (ANSYS Incorporation, Canonsburg, PA, USA) make it a versatile FEA code across various disciplines. The multi-physics attribute of ANSYS allows the same model to be used for a variety of coupled field applications, such as thermal-structural, magneto-structural and electrical-magnetic-flow-thermal. Comprehensive graphical tools are incorporated in ANSYS. These allow for an effective visualisation of the model (Öchsner & Öchsner, 2016). Two essential optimisation types are incorporated in ANSYS and these are design and topology optimisation (Lakshmininarayana, 2004). Pathare et al. (2012a) used ANSYS to study how the strength of corrugated paper containers was affected by different ventilation openings. Maximum stress was observed on containers with the highest ventilation openings (6% of the total area of the container). The authors reported that the stress was produced at top and towards the corner of ventilated opening. Han & Park (2007) used ANSYS FEA code to investigate the principal design parameters of vent holes and hand holes in the faces of corrugated paperboard boxes. Oblong-shaped vent holes performed best in maintaining the strength of the boxes. The results from the model generally agreed well with laboratory experimental results. ANSYS was used by Zhou et al. (1995) to predict the temperature and moisture distribution in food materials during microwave heating. The behaviours and performances of concrete beams (Ibrahim & Mahmood, 2009), dental implants (Kayabaşı et al., 2006) skeletal muscles (Yucesoy et al., 2002), and human ear (Gan et al., 2004) have been studied using ANSYS FEA code. The ANSYS FEA code offers tools such as units awareness, graphical geometry modeller, graphical manual meshing, linear static analysis and nonlinear (large displacement and contact) analysis. ANSYS FEA code is also capable of performing heat transfer, electric, magnetic, fluid flow and fluid structure interaction processes, as well as material models, which include plasticity and creep, among others.
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3.4.2 ABAQUS
ABAQUS (ABAQUS Incorporation, Johnston, RI, USA) is an engineering simulation program based on the finite element method. It can provide the solutions about stress and strain, heat and mass transfer, natural frequencies and mode shape, forced response, fatigue and lifetime estimation and nonlinear material. ABAQUS has been used extensively and widely for many engineering problems due to its numerous attributes such as; containing a comprehensive library of elements that can be used to model any geometry, compatibility with other computer aided design (CAD) software packages, ability to simulate the behaviour of different engineering materials (rubber, polymers, metal, reinforced concrete, composites), capacity to simulate linear, nonlinear, static as well as dynamic analysis. For instance, in a nonlinear analysis using ABAQUS, the load increments and convergence tolerances are automatically chosen to ensure an accurate and efficient solution to the problem. Furthermore, in ABAQUS, when problems involve multiple components, they are modelled by associating the geometry by defining the appropriate material models to each components and specifying the interactions between the components. Hammou et al. (2012) developed an efficient homogenisation model for corrugated paperboard, this model was implemented in the ABAQUS FEA code and the foam behaviour model, which was used to study the drop and shock resistance of corrugated paperboard boxes with different foam cushion internal configurations.
3.4.3 LS-DYNA
LS-DYNA (Livermore Software Technology Corporation, Livermore, CA, USA) is a multi- purpose explicit and implicit FEA code that can be used for analysing real world problems. The origin of LS-DYNA FEA code is highly nonlinear, transient dynamic FEA using explicit time integration. Modelling contact in LS-DYNA is fully automated. In addition, LS-DYNA has the capability to simulate a wide range of different physical phenomena using analysis techniques such as Explicit and Implicit Time Integration Schemes, Nonlinear Dynamics, Large Deformations, Sophisticated Material Models, Complex Contact Conditions, Thermal Analysis and Thermal Structural Coupling, Fluid Dynamics and Fluid Structure Interactions, Smooth Particle Hydrodynamics (SPH), Element Free Galerkin (EFG), Eigenvalue Analysis among others (Lakshmininarayana, 2004). The possibility of increasing computation speed in LS-DYNA helps to improve scalability and various third party software are compatible for pre-processing the input files of LS-DYNA. The pre- and post- processor associated with LS-DYNA is the LS-TAURUS, which was also developed by Livermore Software Technology Corporation. Using LS-DYNA, the mechanical impact loading on the behaviour of consumer structures and products has been extensively studied (Mulkoglu et al., 2015; Neumayer et al., 2006). Venter and Venter (2012) used LS-DYNA to develop numerical models for an inflatable paper dunnage bag. The model was able to predict the inflated shape and the stress condition of the dunnage bag in a constrained void. The error of the numerical model was about 6.2% when the model results were compared with
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physical test results. The drop impact of a cooker with foam packaging and the thermal pre-stress analysis of plastic foil wrapping was performed by Neumayer et al. (2006) using LS-DYNA FEA code. Erdogan and Eksi (2014) used LS-DYNA software to model the thermoforming process of three-thermoformed material and the wall thickness distribution was predicted and compared with experimental results.
3.4.4 MSC MARC
MARC FEA code (MSC Software Corporation, Santa Ana, CA, USA) is a general- purpose tool capable of solving complex structural and thermal problems. It is a robust nonlinear FEA solver with the capabilities to accurately simulate the behaviour of various products under contact, large strain, static, dynamic and multi- physics loading conditions. The pre- and post-processor dedicated to support MARC solver is MENTAT. The combination of MARC and MENTAT enhance the delivery of an efficient and complete analysis (pre-processing and post- processing solution) for an implicit nonlinear FEA (Öchsner & Öchsner, 2016; Lakshmininarayana, 2004). MARC contains an extensive material model library; elastomers, linear elastic, elastic plastic, creep, composites, viscoelastic, hyperelastic, powder metallurgy, among others. Furthermore, MARC contains more than 140 elements which are accurate, modern and robust, hence can be used to represent complex problems appropriately (Lakshmininarayana, 2004). It can handle robust product testing and manufacturing simulation such as predicting damage and crack propagation, acoustics, hydrodynamic bearing, magnetostatics among others. The multi-physics attribute make modelling interactions between structural, electrical, magnetic and thermal analyses possible. MARC is therefore widely considered as complete solution that can tackle all nonlinear simulation requirements (Öchsner & Öchsner, 2016; Lakshmininarayana, 2004). Beex and Peerlings (2009) used MARC to study the creasing and folding behaviour of laminated paperboard. The breaking stress and the deformation behaviour of coated paperboard during indentation with a trapezoidal centre bevel cutter was studied by Nagasawa et al. (2006) using MARC FEA software code.
3.4.5 MSC NASTRAN
NASTRAN (MSC Software Corporation, Santa Ana, CA, USA), known in full as NASA Structural Analysis is an all-purpose FEA solution for various engineering problems ranging from small to complex. MSC Patran is the associated pre- and post-processor for MSC NASTRAN. MSC NASTRAN is widely used to perform static, dynamic, heat transfer, acoustic, thermal, aero-elastic, hydro-elastic, piezo- electric analyses and many more. NASTRAN can handle different material types from metal and plastics to hyperelastic to composites. MSC NASTRAN has a unique element technology, which provides efficient and accurate results, lowering the modelling effort, solution time and computer requirements (Lakshmininarayana, 2004). Biancolini and Brutti (2003) used MSC NASTRAN to evaluate the structural performance of corrugated board panel. In addition, the
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authors reported that the numerical tool (MSC NASTRAN) is applicable to a wide range of problems including corrugated board structure and for product optimisation, because all parameter effects are taken into account, including materials, micro-geometry and macro-geometry. MSC NASTRAN was used by Fadiji et al. (2017) to study the behaviour of paperboard packaging materials under mechanical loadings. The model was able to predict the edge compression resistance of the corrugated paperboard. The authors validated the numerical results with experimental results and close agreement was reported. The experimental results and the simulation results differed by about 5.5%.