An approach for exploring the dynamical behaviour of inhomogeneous structural inclusions under consideration of epistemic uncertainty

Abstract

PurposeThe purpose of this paper is to analyze the wave scattering behaviour of an inhomogeneous and eccentric inclusion in a homogeneous matrix material. Another purpose is to evaluate the influence of epistemic uncertainty on the wave scattering behaviour, particularly on the lack of knowledge about this eccentricity. This task calls for a multidisciplinary model.Design/methodology/approachThe inclusion is modelled as a multi‐layered obstacle, with all layers being eccentric with respect to each other. The material behaviour of the embedding matrix is linear elastic and isotropic. In a multidisciplinary approach, the interaction of the inhomogeneous inclusion and the embedding matrix with respect to an incoming shear wave of arbitrary shape is solved analytically. The purely analytical solution process takes place in the frequency‐domain. Due to the lack of knowledge about the eccentric configuration of the matrix inclusion and its influence on the total wave field inside the matrix material, the mechanical model is coupled with fuzzy set theory for modelling this non‐stochastic uncertainty.FindingsAn analytical model for describing the wave scattering behaviour of an elastic matrix inclusion with eccentric set‐up is found and intimately connected with the framework of fuzzy set theory. Hence it is shown that the treatment of epistemic uncertainty with the derived analytical model is possible and fruitful. Additionally, it is shown that eccentric configurations lead to highly increased amplitudes with respect to the reference case of a concentric or even homogenous set‐up of the inclusion.Originality/valueThe value of this contribution is in the analytical model, which allows one to predict the wave scattering behaviour of eccentric configurations of multi‐layered fibres including the surrounding interphase, and its coupling with fuzzy set theory to cope with the epistemic uncertainty inherent in the geometric set‐up of the matrix inclusion.