A dispersive homogenization model for composites and its RVE existence

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.

Review of Strain Rate Effects of Fiber-Reinforced Polymer Composites

“…At the microscale level, Fish et al [ 77 ] stated that for high rates of loading and a long observation time, internal material interfaces in a heterogeneous material cause reflection and refraction of stress waves, giving rise to dispersion and attenuation of waves within the material microstructure. This phenomenon was further investigated by Liu et al [ 78 ] using a dispersive multiscale numerical model. Elastic wave propagation in a two-dimensional composite microstructure subjected to an incoming sinusoidal wave was considered.…”

“…The micro-scale equation of motion was solved by the perturbation expansion of displacement, inertia and weight functions. This model is adopted in Liu et al [ 78 ], and the application of this method for fiber-reinforced composites is discussed. Karamnejad and Sluys [ 120 ] developed a continuous-discontinuous computational homogenization scheme to capture the micro-scale inertia effects based on the dispersive homogenization model proposed by Fish et al [ 77 ].…”

“… The DNS model mesh of a composite structure consisting of 100 repeating unit microstructure cell. There are two phases of materials, circular inclusions with a diameter of 0.5 mm and a surrounding matrix [ 78 ]. …”

A numerical homogenization scheme used for derivation of a homogenized viscoelastic-viscoplastic model for the transverse response of fiber-reinforced polymer composites

“…i jkl : ε e kl (t n+1 ) + D ve i jkl (∆t) : ∆ε e kl + σ hist i j (t n ) (49) By taking the derivative of the stress σ i j (t n+1 ) with respect to the strain ε e kl (t n+1 ), the consistent tangent can be derived as:…”

“…A discrete element method generator called HADES is used to generate a stochastic distribution of the fibers with the diameter D f = 5 µm and a minimum distance between fibers d min = 0.2 µm, following the procedures in Liu et al[49]. After this, a mesh is generated with GMSH[50] for the fibers and the matrix.…”