Nonlinear micromechanics of open-cell cellular solids

Doctoral thesis, 2008

An approach for modelling the response of open-cell cellular solids at finite strains is developed. The model framework comprises a mechanistic formulation where the cellular solid is considered as a network of struts, each connecting two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle in compression. Owing to this simple ansatz, important material behaviour, such as the linear-elastic response and plateau behaviour, are easily captured. Other important phenomena, such as initial anisotropy and deformation induced anisotropy are inherent within the method, and it is possible to include multiple nonlinear mechanisms, such as hyperelasto-(visco)plasticity and damage, in a straightforward fashion. First, a hyperelastic equation is developed in order to evaluate the suggested kinematic approach. The model is implemented at material point level. The model parameters are identified for a flexible, open-cell, polyeter urethane foam and the equation is validated against a variety of experiments. Next, a micropolar hyperelastic model is proposed for capturing length-scale effects associated with couples carried by the struts. The model’s capability is demonstrated through numerical simulations. Finally, an approach for capturing the inelastic response is presented. Here, the resulting equations are evaluated against experiments on both material point and component level with respect to an open-cell aluminium alloy foam.