Estimating fibres’ material parameter distributions from limited data with the help of Bayesian inference

Abstract Numerous materials are essentially structures of discrete fibres, yarns or struts. Considering these materials at their discrete scale, one may distinguish two types of intrinsic randomness that affect the structural behaviours of these discrete structures: geometrical randomness and material randomness. Identifying the material randomness is an experimentally demanding task, because many small fibres, yarns or struts need to be tested, which are not easy to handle. To avoid the testing of hundreds of constituents, this contribution proposes an identification approach that only requires a few dozen of constituents to be tested (we use twenty to be exact). The identification approach is applied to artificially generated measurements, so that the identified values can be compared to the true values. Another question this contribution aims to answer is how precise the material randomness needs to be identified, if the geometrical randomness will also influence the macroscale behaviour of these discrete networks. We therefore also study the effect of the identified material randomness to that of the actual material randomness for three types of structures; each with an increasing level of geometrical randomness.

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