Dynamic behaviour of low- to high-density anisotropic cellular materials

The dynamic behaviour of a novel anisotropic cellular micro-structural geometry derived from the basic symmetric Kelvin cell is discussed for varying relative density. The cells are arranged in a cubic array and the dynamic response is studied in a classical seismic mass setup using beam elements to represent the ligaments of the cell. The eigenfrequencies and the eigenmodes of the cellular array are computed together with forced response simulations where a proportional damping model of the Young's modulus for the cell ligaments is assumed. The frequency dependence of the damping is based on a fractional derivative representation. Using a recently developed inversion method, equivalent, homogenised solid material models of the cellular array are discussed with the associated equivalent elastic properties given in terms of the 21 elastic constants of the Hooke's tensor. For the equivalent solid material models, the eigenfrequencies and eigenmodes are computed, and forced response simulations are performed assuming the same type of proportionality in the damping as the cellular array, for the same seismic mass setup. The correlation, between the eigenfrequencies and the eigenmodes, shows an overall interesting agreement between the cellular and the equivalent solid model for the quite complex deformation shapes observed. The forced response results indicate that the equivalent solid modelling accurately represents the global dynamics of the anisotropic cellular array, but needs to be further refined when local shearing deformation within the individual cells starts to be dominating.
QC 20221024