Abstract
An asymptotic homogenization model considering wave dispersion in composites is investigated. In this approach, the effect of the microstructure through heterogeneity-induced wave dispersion is characterised by an acceleration gradient term scaled by a “dispersion tensor”. This dispersion tensor is computed within a statistically equivalent representative volume element (RVE). One-dimensional and two-dimensional elastic wave propagation problems are studied. It is found that the dispersive multiscale model shows a considerable improvement over the non-dispersive model in capturing the dynamic response of heterogeneous materials. To test the existence of an RVE for a realistic microstructure for unidirectional fiber-reinforced composites, a statistics study is performed to calculate the homogenized properties with increasing microstructure size. It is found that the convergence of the dispersion tensor is sensitive to the spatial distribution pattern. A calibration study on a composite microstructure with realistic spatial distribution shows that convergence is found although only with a relatively large micromodel.
Highlights
The heterogeneity of the microstructure of composite materials causes dispersion in wave propagation associated with dynamic loading
It is found that the dispersion effect can be characterized by a dispersion tensor, the magnitude of which is dependent on the material property contrast of inclusion/matrix and the size of the inclusion
Comparison with a direct numerical simulation (DNS) model shows that the dispersive multiscale model has a significantly improved accuracy, compared with non-dispersive homogenized models
Summary
The heterogeneity of the microstructure of composite materials causes dispersion in wave propagation associated with dynamic loading. Recent development of generalized homogenization models enrich the macroscale displacement with additional generalized degrees of freedom of Bloch modes following the lines of Willis’ model, see Sridhar et al [15] These methods are suitable for linear elastic (layered) periodic materials while an extension to materials with random microstructure is not always straightforward. A dispersive multiscale model based on asymptotic homogenization is reviewed and the existence of an RVE for this method for unidirectional fiber-reinforced composites is investigated. 2, the dispersive model based on asymptotic homogenization technique is introduced The accuracy of this numerical method for 1D and 2D elastic wave propagation is demonstrated in Sect.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call