The nonlinear elasticity of cellular bodies under large deformations

Abstract

Many natural and man-made cellular bodies are light-weight, shock-absorbing, multifunctional materials, capable of undertaking large elastic deformations. These properties are due to a complex system of local deformations which can lead to changes in the material properties as the deformation progresses, but their study is nontrivial since the corresponding stresses are non-trivial functions of volume fraction, micro-geometry, and material properties of the components. For cellular bodies of hyperelastic material, several main factors determine the magnitude of the stress level, including the cell geometry, the cell wall thickness, and the presence of cell inclusions. In this thesis, two nonlinear elastic parameters are identied, namely a nonlinear elastic modulus and a nonlinear Poisson's ratio, which are dened in terms of the large stresses and strains in the elastic cell walls, and their utility in estimating how dierent competing factors may contribute to the complex mechanical behaviour of cellular structures is investigated. For the numerical analysis, nite element simulations of periodic, honeycomb-like structures with a small number of square, diamond, or hexagonal cells made from a nonlinear hyperelastic material are presented. This study oers important insight into the fundamental behaviour of cellular structures of nonlinear elastic material under large strains, and contributes to illuminate key mechanical eects that are not visible under small strains.