Why Laguerre tessellations are good approximations of foams

Abstract eng:
Stochastic models are valuable tools to study the mechanical behaviour of low-density foams. Owing to a similar cellular morphology, Laguerre tessellations have turned out to be the natural model for such foams. Laguerre tessellations are additively weighted generalisations of Voronoi tessellations, where polyhedral cells are formed through interaction of spheres. However, the cell curvature of foams allows only an approximation by Laguerre tessellations. This work studies the error in elasticity induced by the approximation based on simulated random foams. For low polydispersities, Young’s modulus is overpredicted with an almost constant error of at most5 % by the Laguerre approximations. With increasing polydispersity the prediction error increases following a cubic function.

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