A constitutive equation for open-cell cellular solids, including viscoplasticity, damage and deformation induced anisotropy

A thermodynamically consistent approach is developed for modelling the response of an open-cell cellular solid at finite compressive strains. The cellular solid is considered as a network of struts, where each strut connects two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle plastically. The strut deformation is assumed to be 1-dimensional and depend directly on the macroscopic deformation; thus the description of the strut response requires only a scalar valued response function. Owing to this simple ansatz it is possible to include multiple nonlinear mechanisms, such as hyperelasto-viscoplasticity and damage. The macrostress is obtained by averaging over a statistical ensemble of struts. The model has been implemented in the context of finite strains and damage coupled to viscoplastic Perzyna type behaviour. All model parameters may be determined by performing tests in simple compression. The model is well capable of reproducing data from compression experiments on various open-cell aluminium foams.