3D MORPHOLOGICAL MODELLING OF A RANDOM FIBROUS NETWORK

Abstract

In the framework of the Silent Wall ANR project, the CMM and the US2B are associated in order to characterize and to model fibrous media studying 3D images acquired with an X-Ray tomograph used by the US2B. The device can make 3D images of maximal 23043 voxels with resolutions in the range of 2 μm to 15 μm. Using mathematical morphology, measurements on the 3D X-Ray CT images are used to characterize materials. For example measuring the covariance on these images of an acoustic insulating material made of wooden fibres highlights the isotropy of the fibres orientations in the longitudinal planes which are perpendicular to the compression Oz axis. Moreover, it is possible to extract other morphological properties from these image processing methods such as the size distribution either of the fibres or of the pores by estimating the morphological opening granulometry of the considered medium. Using the theory of random sets introduced by Georges Matheron in the early 1970's, the aim of this work is to model such a fibrous material by parametric random media in 3D according to the prior knowledge of its morphological properties (covariance, porosity, size distributions, etc.). A Boolean model of random cylinders in 3D stacked in planes parallel to each other and perpendicular to the Oz compression axis is first considered. The granulometry results provide gamma distributions for the radii of the fibres. In addition, a uniform distribution of the orientations is chosen, according to the experimental isotropy measurements in the longitudinal planes. Finally the third statistical factor is the length distribution of the fibres which can be fitted by an exponential distribution. Thus it is possible to estimate the validity of this model first by trying to fit the experimental transverse and longitudinal covariances of the pores with the theoretical ones taking into account the statistical distributions of the dimensions of the random cylinders. The second method to validate the model consists in comparing morphological measurements (density profiles, covariance, opening granulometry, tortuosity, specific surface area) processed on real and on simulated media.