Computer modelling of cellular structures under uniaxial loading
Hayley Wyatt  1, *@  , Khulud Alayyash  1@  , Muhammad Rahman  2@  , Sam Evans  2@  , Angela Mihai  1@  
1 : Cardiff University, School of Mathematics
Senghennydd Road, Cardiff -  United Kingdom
2 : Cardiff University, School of Engineering
The Parade, Cardiff -  United Kingdom
* : Corresponding author

In many natural load-bearing cellular structures, support requirements are typically met through a combination of increase in cell number or size and sustained sclerification of the cell walls. For example, dicotyledon stems (e.g. magnolias) increase their diameter primarily by cell division, while monocotyledon stems (e.g. lilies) prevent mechanical failure through a combination of initiation of growth with a stem and increased strength by sustained cell wall expansion and lignification. For living cellular structures, there are many physiological and ecological factors that determine their material properties and influence their mechanical support system. For structures with uniform cell size, wall thickness, and shape, the fundamental question arises whether the same volume of cell wall material has the same effect when arranged as many small cells or as fewer large cells. A combination of finite element modelling (FEM) and experimental work has been conducted to investigate the effect of the number of cells for a fixed volume of material for nonlinear cellular structures under uniaxial tension. Three different structure geometries (stacked, staggered and diamond) were analysed computationally. Each FEM was created within the FEBio software suite, with variations of the different geometries analysed to investigate the effect of the number of cells. Each structure was modelled using a neo-Hookean and a Mooney-Rivlin material model, with a mesh refinement study conducted for each model variation. For all structures analysed (including both material models) the results from the computational models suggest that the overall stiffness of the cellular structure increases as the number of cells increases for a fixed material volume. Experimentally, digital image correlation (DIC) was used to investigate the behaviour of silicone cellular structures under uniaxial tension. This allowed displacement and strain maps to be created over the material surface, showing the local deformations for the cell walls, whilst also considering the overall behaviour of the structures. The experimental results were then compared to the FEM results, allowing validation of the model results. 

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