Finite element modelling of the mechanics of solid foam materials

Abstract: Failure of bi-material interfaces is studied with the aim to quantify the influence of the induced stress concentrations on the strength of the interfaces. A simple point-stress criterion, used in conjunction with finite element calculations, is evaluated to provide strength predictions for bi-material bonded joints and inserts in polymer foam. The influence of local stress concentrations on the initiation of fracture at open and closed wedge bi-material interfaces is investigated. The joint combinations are analysed numerically and the strength predictions obtained from the point-stress criterion are verified in experiments. The predictions are made using a simple point-stress criterion in combination with highly accurate finite element calculations. The point-stress criterion was known from earlier work to give accurate predictions of failure at cracks and notches but had to be slightly modified to become applicable for the studied configurations. The criterion showed to be generally applicable to the bi-material interfaces studied herein. Sensible predictions for the tendentious strength behaviour could be made with reasonable accuracy, including the prediction of crossover from local, joint-induced failure to global failure. To study the micromechanical properties of a cellular solid with arbitrary topology, various models of a closed-cell foam are created on the basis of random Voronoi tessellations. The foam models are analysed using the finite element method and the effective elastic properties of the model cellular solids are determined. The calculated moduli are compared to the properties of a real reference foam and the numerical results show to be in very good agreement. The mechanical properties of closed-cell, low-density cellular solids are governed by the stiffnesses of the cell edges and the cell faces. Models of idealised foam models with planar cell faces, cannot account for the curved faces found on some metal and polymer foams. Finite element models of closed-cell foams were created to analyse the influence of cell face curvature on the stiffness of the foam. By determining the elastic modulus for foams with non-planar cell faces, the effect of cell face curvature could be analysed as a function of the relative density and the distribution of solid material between cell edges and faces. Foam models were generated from disturbed point distribution lattices and compared to models obtained from random distributions. The aim was to analyse if and how the geometry of the cells and their spatial arrangement influences the mechanical properties of a foam. The results suggest that the spatial arrangement and the geometry of the cells have significant influence on the properties of a foam. The elastic properties calculated for models from disturbed foam structures underestimated the elastic moduli of the foam, whereas models from random structures provided results which were in very good agreement with a reference foam.