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

• Published in: Journal of engineering mathematics Vol. 109; no. 1; pp. 3 - 19
• Main Authors: Mihai, L. Angela, Safar, Alexander, Wyatt, Hayley
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.04.2018; Springer Nature B.V
• Subjects: Aging (natural); Applications of Mathematics; Cellular structure; Computational Mathematics and Numerical Analysis; Debonding; Deformation mechanisms; Fiber composites; Finite element method; Hexagonal cells; Internal pressure; Lamella; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Mechanical properties; Periodic structures; Separation; Shear deformation; Theoretical and Applied Mechanics; Vegetables; Walls; Cellular solids; Finite element method; Unilateral contact; Large strain deformation; Hyperelastic materials; Fruit softening
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-016-9894-2

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).