Debonding of cellular structures with fibre-reinforced cell walls under shear deformation

Abstract

Many natural structures are cellular solids at millimetre scale and fibre-reinforced composites at micrometre scale. For these structures, mechanical properties are associated with cell strength, and phenomena such as cell separation through debonding of the middle lamella in cell walls are key in explaining some important characteristics or behaviour. To explore such phenomena, we model cellular structures with non-linear hyperelastic cell walls under large shear deformations, and incorporate cell wall material anisotropy and unilateral contact between neighbouring cells in our models. Analytically, we show that, for two cuboid walls in unilateral contact and subject to generalised shear, gaps can appear at the interface between the deforming walls. Numerically, when finite element models of periodic structures with hexagonal cells are sheared, significant cell separation is captured diagonally across the structure. Our analysis further reveals that separation is less likely between cells with high internal cell pressure (e.g. in fresh and growing fruit and vegetables) than between cells where the internal pressure is low (e.g. in cooked or ageing plants).

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

“…Solid cellular bodies, or foams, are ubiquitous in nature and engineering applications, and can be found in both load-and non-load-bearing structures [8,[123][124][125][126][127]. For soft cellular structures with components exhibiting material nonlinear elasticity, bridging the microstructural responses of individual cells with the apparent macrostructural behaviour is a challenging modelling problem in materials science.…”

A Microstructure-Based Hyperelastic Model for Open-Cell Solids

“…Under uniform stresses, many isotropic materials deform uniformly [29,30,33], whereas in cellular structures, the deformation generally concentrates in regions that are more easily deformable. The hyperelastic models developed here capture structural behaviors at a mesoscopic level, where the number of cells is finite and the size of the structure is comparable to the cell-size, and can be useful as an initial approximation in multilevel approaches, whereby a cellular structure is represented first as an elastic material deforming uniformly, and after the loading is increased, the areas where the stress field reaches critical values are remodelled as individual cells to predict critical local effects [31].…”

Causal factors concerning the texture of French fries manufactured at industrial scale

“… (Possible) cause Models Ref. Complexity Molecular level Pectin chemistry Kinetic model Verlinden and De Baerdemaeker (1997) + PME activity Kinetic model Moens et al (2021) , van Dijk and Tijskens (2003) + Syneresis WHC model/Flory Rehner Van der Sman et al (2013) ++ Starch gelatinization Flory-Huggins Van der Sman and Meinders (2011) + Starch retrogradation Lauritzen-Hoffman Farhat et al (2000) + Cellular level Cell swelling hyperelastic model Van der Sman (2015b) ++ Cell separation FEM/SPH-DEM Paul Van Liedekerke et al (2010) , ( 2011 ), Mihai et al (2018) ++++ Cell wall strength/stress Cell model Van der Sman (2015b) ++ Starch swelling Cell model Van der Sman and Meinders (2011) ++ Microstructural level Core structure Multiscale – ++++ Ice formation Phase field …”

“…Cell adhesion is accounted for in the model of the mechanics of cellular tissue of ripened apples ( Paul Van Liedekerke et al, 2011 ), which uses a SPH/DEM multiscale modelling technique, which is a rather computational intensive technique. A more feasible model of debonding between adhering cells is described in ( Mihai et al, 2018 ), which follows the more commonly used Finite Elements Method (FEM). Here, cells are approximated as 2D-hexagonal units, with fiber-reinforced cell walls, and internal pressure (due to turgor).…”