Uncertainty quantification for metal foam structures by means of image analysis

Abstract A metal foam may consist of a very heterogeneous structure, such that the size of the representative volume element is rather large. Therefore, macroscopic properties of components made of metal foams might show a large scatter. To predict the scatter of eigenfrequencies for bending beam structures, a consistent formulation from image analysis to the distribution of macroscopic properties is developed. With the help of computed tomography, statistical characteristics of the cell geometry of open cell foams are estimated. This information allows to fit a random tessellation model to the material, which reproduces the statistical properties of the cell geometry. To compute the linear elastic properties as well as the mass density of metal foams, three dimensional volume elements from random model realizations are analyzed and distributions of apparent properties are computed. The covariance function is estimated by considering volume elements at different locations of the macrostructure. Having a description of random fields for the apparent properties at hand, Monte Carlo simulations are applied to predict the eigenfrequencies, their scatter and the associated eigenforms of beams made of metal foams. The procedure is validated by experiments.

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