Open-cell Aluminum foam compression simulation using 3-D Voronoi diagram model

3-D Voronoi diagram model used to simulate the compression response of open-cell Aluminum foam core material, which is loaded in a sandwich structure. 3-D Voronoi model had been carried out to accurately represent the real characteristics of Aluminum foam. Model was enhanced by increasing number of foam cells relative to unit volume,  taking into account not only plastic properties of material forming of Voronoi struts but also plastic properties. In addition, Johnson-Cook model was encapsulated in the model to define plastic properties. The advantages of using Johnson-Cook model is that the developed model can be simulated at different strain rates. This improved model validated using results from previous experimental and mathematical works. Different relative densities and regularities are used in simulations in order to study the effect of them on stress-strain curve.  For the present case study, the finite-element package Abaqus/Standard was used. In the pre-processing stage, the model geometry is obtained by the developed model generation by C++ Code. THis code provide geometry in IGS file format which imported to Abaqus. In the presented model,the material was modeled as an elastoplastic material. The elastic properties were defined by isotropic hardening model. The elastic properties are completely defined by Young's modulus and Poisson's ratio of Al-6061-T6. The plastic properties were defined by Johnson-Cook model. Boundary conditions were applied to the upper and lower plate. The upper plate and the lower plate were allowed to move only in one direction perpendicular to each other.  Equal and opposite displacement were applied to plates in this direction. Voronoi ligaments were discretized with spatial beam elements B32 in Abaqus. Quadratic interpolation was used. In order to avoid divergence of solution due to small ligaments, especially in high irregularities models, two elements per ligaments were used. The upper and lower plates were discretized with four-node Shell elements. They are generated to coincide with nodes in the beams. The general static method was selected to capture changes in reaction forces and displacement of upper and lower plates. In general static method, non-linear effects were activated due to large deformations, which were expected during simulations. In order to improve convergence rate of the solution, automatic stabilization was used by specifying dissipation energy fraction with value equal  and by using adaptive stabilization with a maximum ratio of stabilization to strain energy with value equal 0.05. In the post-processing stage, at every step of the solution, forces at every element of lower plate were added to form the total reaction force. Displacements of lower plate and upper plate were added to form total displacement. In order to draw stress-stain curve, total reaction force was divided by cross section area of aluminum foam cube to form stress. Displacement was divided by the original length of aluminum foam cube to form strain.