Multi-scale identification of the viscoelastic behaviour of composite materials through a non-destructive test

Abstract The problem of characterising the viscoelastic behaviour of a composite material, at each pertinent scale, is addressed in this paper. To this purpose, a dedicated multi-scale identification strategy (MSIS), exploiting the information restrained in the macroscopic non-linear dynamic response of the composite, is developed. The MSIS aims to identify the viscoelastic behaviour of the composite at both mesoscopic (lamina-level) and microscopic (constitutive phases level) scales. This goal can be achieved by solving an inverse problem, wherein the identification of the parameters tuning the viscoelastic behaviour of the constitutive phases is obtained by minimising the distance between the numerical and the reference harmonic (macroscopic) responses of the composite; Of course, pertinent constraints on the natural damped frequencies as well as on the positive definiteness of the stiffness tensor of each phase must be provided. The MSIS relies on: (i) a general homogenisation procedure based on the strain energy of periodic media generalised to the case of viscoelastic materials; (ii) a dedicated solver to deal with the non-linear modal and harmonic analyses of the multilayer plate at the macroscopic scale; (iii) the Bagley-Torvik viscoelastic model to describe the viscoelastic behaviour of the matrix; (iv) a general hybrid optimisation algorithm able to deal with optimisation problems defined over a domain of variable dimension to solve the inverse problem. The effectiveness of the MSIS is proven through a suitable benchmark.

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